[AHJR] Achar, P. N., Henderson, A., Juteau, D. and Riche, S., Modular generalized Springer correspondence: an overview. See arXiv:1510.08962.Google Scholar

[Ac02] Ackermann, B., A short note on Howlett-Lehrer theory. Arch. Math. (Basel) 79 (2002), 161–166.Google Scholar

[ALTV] Adams, J. D., van Leeuwen, M., Trapa, P. E. and Vogan, D. A., Unitary representations of real reductive groups. See arXiv:1212.2192.Google Scholar

[Al09] Allcock, D., A new approach to rank one linear algebraic groups. J. Algebra 321 (2009), 2540–2544.Google Scholar

[Al79] Alvis, D., The duality operation in the character ring of a finite Chevalley group. Bull. Amer. Math. Soc. (N.S.) 1 (1979), 907–911.Google Scholar

[Al82] Alvis, D., Duality and character values of finite groups of Lie type. J. Algebra 74 (1982), 211–222.CrossRefGoogle Scholar

[AlLu82] Alvis, D. and Lusztig, G., The representations and generic degrees of the Hecke algebras of type H₄ . J. Reine Angew. Math. 336 (1982), 201–212; Erratum, 449 (1994), 217–218.Google Scholar

[As] Asai, T., Endomorphism algebras of the reductive groups over F_q of classical type. Unpublished manuscript (around 1980).Google Scholar

[As84a] Asai, T., Unipotent class functions of split special orthogonal groups over finite fields. Comm. Algebra 12 (1984), 517–615.Google Scholar

[As84b] Asai, T., The unipotent class functions on the symplectic groups and odd orthogonal groups over finite fields. Comm. Algebra 12 (1984), 617–645.Google Scholar

[As84c] Asai, T., The unipotent class functions of exceptional groups over finite fields. Comm. Algebra 12 (1984), 2729–2857.CrossRefGoogle Scholar

[As85] Asai, T., The unipotent class functions of non-split finite special orthogonal groups. Comm. Algebra 13 (1985), 845–924.Google Scholar

[Asch00] Aschbacher, M., The classification of the finite simple groups. Jber. d. Dt. Math.-Verein 102 (2000), 95–101.Google Scholar

[Asch04] Aschbacher, M., The status of the classification of the finite simple groups. Notices of the AMS 51 (2004), 736–740.Google Scholar

[BBD82] Beilinson, A. A., Bernstein, J. and Deligne, P., Faisceaux pervers. Astérisque No. 100, Soc. Math. France, 1982.Google Scholar

[Be79] Benson, C., The generic degrees of the irreducible characters of E₈. Comm. Algebra 7 (1979), 1199–1209.Google Scholar

[BeCu72] Benson, C. and Curtis, C. W., On the degrees and rationality of certain characters of finite Chevalley groups. Trans. Amer. Math. Soc. 165 (1972), 251–273; Corrections and additions: ibid. 202 (1975), 405–406.Google Scholar

[BeLu78] Beynon, W. M. and Lusztig, G., Some numerical results on the characters of exceptional Weyl groups. Math. Proc. Cambridge Philos. Soc. 84 (1978), 417– 426.Google Scholar

[BeSp84] Beynon, W. M. and Spaltenstein, N., Green functions of finite Chevalley groups of type E_n (n = 6, 7, 8). J. Algebra 88 (1984), 584–614.Google Scholar

[Bo98] Bonnafé, C., Formule de Mackey pour q grand. J. Algebra 201 (1998), 207–232.Google Scholar

[Bo99] Bonnafé, C., Produits en couronne de groupes linéaires. J. Algebra 211 (1999), 57–98.Google Scholar

[Bo00] Bonnafé, C., Mackey formula in type A. Proc. London Math. Soc. 80 (2000), 545–574; Erratum, ibid. 86 (2003), 435–442.Google Scholar

[Bo05] Bonnafé, C., Quasi-isolated elements in reductive groups. Comm. Algebra 33 (2005), 2315–2337.CrossRefGoogle Scholar

[Bo06] Bonnafé, C., Sur les caractères des groupes réductifs finis à centre non connexe: applications aux groupes spéciaux linéaires et unitaires. Astérisque No. 306 (2006).Google Scholar

[Bo11] Bonnafé, C., Representations of SL₂ (F_q). Algebra and Applications, 13. Springer-Verlag London, 2011.Google Scholar

[BDR15] Bonnafé, C., Dat, J.-F. and Rouquier, R., Derived categories and Deligne–Lusztig varieties II. Ann. of Math. (2) 185 (2017), 609–670.Google Scholar

[BoMi11] Bonnafé, C. and Michel, J., Computational proof of the Mackey formula for q > 2. J. Algebra 327 (2011), 506–526.Google Scholar

[BoRo93] Bonnafé, C. and Rouquier, R., Catégories dérivées et variétés de Deligne-Lusztig. Publ. Math. Inst. Hautes Études Sci. 97 (2003), 1–59.Google Scholar

[Bor91] Borel, A., Linear Algebraic Groups. Second enlarged edition. Graduate Texts in Mathematics vol. 126, Springer Verlag, Berlin–Heidelberg–New York, 1991.Google Scholar

[Bor70] Borel, A., Carter, R., Curtis, C. W., Iwahori, N., Springer, T. A. and Steinberg, R., Seminar on Algebraic Groups and Related Algebraic Groups. Lecture Notes in Mathematics, vol. 131. Springer Verlag, Berlin–New York, 1970.Google Scholar

[BoTi65] Borel, A. and Tits, J., Groupes réductifs. Publ. Math. IHES 27 (1965), 55–150.Google Scholar

[Bou68] Bourbaki, N., Groupes et algèbres de Lie, Chap. 4, 5 et 6. Hermann, Paris, 1968.Google Scholar

[Bou07] Bourbaki, N., Algèbre, Chap. 9. Springer Verlag, Berlin Heidelberg, 2007.Google Scholar

[Bre18] Breuer, T., The GAP character table library. Online available at www.math.rwth-aachen.de/~Thomas.Breuer/ctbllib/index.html.Google Scholar

[Br17] Broué, M., On Characters of Finite Groups. Springer Verlag, Heidelberg, 2017.Google Scholar

[BrKi02] Broué, M. and Kim, S., Familles de caractères des algèbres de Hecke cyclotomiques. Adv. Math. 172 (2002), 53–136.Google Scholar

[BrMa92] Broué, M. and Malle, G., Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis. Math. Ann. 292 (1992), 241–262.Google Scholar

[BrMa93] Broué, M. and Malle, G., Zyklotomische Hecke-Algebren. Astérisque No. 212 (1993), 119–189.Google Scholar

[BMM93] Broué, M., Malle, G. and Michel, J., Generic blocks of finite reductive groups. Astérisque No. 212 (1993), 7–92.Google Scholar

[BMM99] Broué, M., Malle, G. and Michel, J., Towards spetses, I. Transform. Groups 4 (1999), 157–218.CrossRefGoogle Scholar

[BMM14] Broué, M., Malle, G. and Michel, J., Split spetses for primitive reflection groups. Astérisque No. 359 (2014).Google Scholar

[BrMi89] Broué, M. and Michel, J., Blocs et séries de Lusztig dans un groupe réductif fini. J. Reine Angew. Math. 395 (1989), 56–67.Google Scholar

[BrLu12] Brunat, O. and Lübeck, F., On defining characteristic representations of finite reductive groups. J. Algebra 395 (2013), 121–141.Google Scholar

[Ca88] Cabanes, M., Brauer morphism between modular Hecke algebras. J. Algebra 115 (1988), 1–31.Google Scholar

[Ca13] Cabanes, M., On Jordan decomposition of characters for SU(n, q). J. Algebra 374 (2013), 216–230.Google Scholar

[CE94] Cabanes, M. and Enguehard, M., On unipotent blocks and their ordinary characters. Invent. Math. 117 (1994), 149–164.CrossRefGoogle Scholar

[CE99] Cabanes, M. and Enguehard, M., On blocks of finite reductive groups and twisted induction. Adv. Math. 145 (1999), 189–229.Google Scholar

[CE04] Cabanes, M. and Enguehard, M., Representation Theory of Finite Reductive Groups. New Mathematical Monographs, 1. Cambridge University Press, 2004.Google Scholar

[CaSp17] Cabanes, M., Späth, B., Inductive McKay condition for finite simple groups of type C. Represent. Theory 21 (2017), 61–81.Google Scholar

[Car55-56] Cartan, H., Variétés Algébriques Affines. Séminaire Henri Cartan, vol. 8 (1955-1956), Exp. No. 3, 12 pp. Available at www.numdam.org/item?id=SHC_1955-1956_8_A3_0Google Scholar

[Ca72] Carter, R. W., Simple Groups of Lie Type. Wiley, New York, 1972; reprinted 1989 as Wiley Classics Library Edition.Google Scholar

[Ca85] Carter, R. W., Finite Groups of Lie Type: Conjugacy Classes and Complex Characters. Wiley, New York, 1985; reprinted 1993 as Wiley Classics Library Edition.Google Scholar

[Ca95] Carter, R. W., On the representation theory of the finite groups of Lie type over an algebraically closed field of characteristic 0. Algebra, IX, pp. 1–120, 235–239, Encyclopaedia Math. Sci., 77, Springer, Berlin, 1995.Google Scholar

[Cha68] Chang, B., The conjugate classes of Chevalley groups of type G₂. J. Algebra 9 (1968), 190–211.Google Scholar

[ChRe74] Chang, B. and Ree, R., The characters of G₂ (q). Symposia Mathematica, Vol. XIII (Convegno di Gruppi e loro Rappresentazioni, INDAM, Rome, 1972), pp. 395– 413. Academic Press, London, 1974.Google Scholar

[Ch55] Chevalley, C., Sur certains groups simples. Tôhoku Math. J. 7 (1955), 14–66.Google Scholar

[Ch05] Chevalley, C., Classification des Groupes Algébriques Semi-simples. Collected works. Vol. 3. Edited and with a preface by Cartier, P.. With the collaboration of Cartier, A. Grothendieck and M. Lazard. Springer-Verlag, Berlin, 2005.Google Scholar

[Chl09] Chlouveraki, M., Blocks and Families for Cyclotomic Hecke Algebras. Lecture Notes in Mathematics, 1981. Springer-Verlag, Berlin, 2009.Google Scholar

[Chl10] Chlouveraki, M., Rouquier blocks of the cyclotomic Hecke algebras of G(de, e, r). Nagoya Math. J. 197 (2010), 175–212.Google Scholar

[ClPr13] Clarke, M. C. and Premet, A., The Hesselink stratification of nullcones and base change. Invent. Math. 191 (2013), 631–669.Google Scholar

[CMT04] Cohen, A. M., Murray, S. H. and Taylor, D. E., Computing in groups of Lie type. Math. Comp. 73 (2004), 1477–1498.Google Scholar

[Con14] Conrad, B., Reductive group schemes. Autour des Schémas en Groupes. Vol. I, pp. 93–444, Panor. Synthèses, 42/43, Soc. Math. France, Paris, 2014.Google Scholar

[CCNPW] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of Finite Groups. Oxford University Press, London/New York, 1985.Google Scholar

[Cu66] Curtis, C. W., The Steinberg character of a finite group with a (B, N)-pair. J. Algebra 4 (1966), 433–441.Google Scholar

[Cu80] Curtis, C. W., Truncation and duality in the character ring of a finite group of Lie type. J. Algebra 62 (1980), 320–332.Google Scholar

[Cu88] Curtis, C. W., Representations of Hecke algebras. Astérisque 168 (1988), 13–60.Google Scholar

[CuRe81] Curtis, C. W. and Reiner, I., Methods of Representation Theory Vol. I. Wiley, New York, 1981.Google Scholar

[CuRe87] Curtis, C. W. and Reiner, I., Methods of Representation Theory Vol. II. Wiley, New York, 1987.Google Scholar

[DeLu76] Deligne, P. and Lusztig, G., Representations of reductive groups over finite fields. Ann. of Math. (2) 103 (1976), 103–161.Google Scholar

[DeLu82] Deligne, P. and Lusztig, G., Duality for representations of a reductive group over a finite field. J. Algebra 74 (1982), 284–291.CrossRefGoogle Scholar

[DeLu83] Deligne, P. and Lusztig, G., Duality for representations of a reductive group over a finite field. II. J. Algebra 81 (1983), 540–545.Google Scholar

[DG70/11] Demazure, M. and Grothendieck, A. (eds.), Séminaire de Géométrie Algébrique du Bois Marie - 1962-64 - Schémas en groupes - (SGA 3) - Tome III (Structure des schémas en groupes réductifs). Édition recomposée et annotée du volume 153 des Lecture Notes in Mathematics publié en 1970 par Springer-Verlag. Documents Mathématiques, vol. 8, Soc. Math. France, 2011.Google Scholar

[DN19] De Medts, T. and Naert, K., Suzuki–Ree groups as algebraic groups over . See arXiv:1904.10741.Google Scholar

[Der84] Deriziotis, D. I., Conjugacy Classes and Centralizers of Semisimple Elements in Finite Groups of Lie Type. Vorlesungen aus dem Fachbereich Mathematik der Universität GH Essen, 11. Universität Essen, Fachbereich Mathematik, Essen, 1984.Google Scholar

[DeMi87] Deriziotis, D. I. and Michler, G. O., Character table and blocks of finite simple triality groups ³D₄ (q). Trans. Amer. Math. Soc. 303 (1987), 39–70.Google Scholar

[Dieu74] Dieudonné, J., La Géométrie des Groupes Classiques (troisième édition). Springer Verlag, Berlin–Heidelberg–New York, 1974.Google Scholar

[Di87] Digne, F., Shintani descent and L functions on Deligne-Lusztig varieties. The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), pp. 61–68, Proc. Sympos. Pure Math., 47, Part 1, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

[DiMi83] Digne, F. and Michel, J., Foncteur de Lusztig et fonctions de Green généralisées. C. R. Acad. Sci. Paris Sér. I Math. 297 (1983), 89–92.Google Scholar

[DiMi85] Digne, F. and Michel, J., Fonctions L des variétés de Deligne–Lusztig et descente de Shintani. Mém. Soc. Math. France, no. 20, suppl. au Bull. S. M. F. 113, 1985.Google Scholar

[DiMi90] Digne, F. and Michel, J., On Lusztig’s parametrization of characters of finite groups of Lie type. Astérisque No. 181–182 (1990), 113–156.Google Scholar

[DiMi94] Digne, F. and Michel, J., Groupes réductifs non connexes. Ann. scient. Éc. Norm. Sup. 27 (1994), 345–406.Google Scholar

[DiMi14] Digne, F. and Michel, J., Parabolic Deligne-Lusztig varieties. Adv. Math. 257 (2014), 136–218.Google Scholar

[DiMi15] Digne, F. and Michel, J., Complements on disconnected reductive groups. Pacific J. Math. 279 (2015), 203–228.Google Scholar

[DiMi20] Digne, F. and Michel, J., Representations of Finite Groups of Lie Type. London Mathematical Society Student Texts, 21. 2nd Edition, Cambridge University Press, 2020, to appear.Google Scholar

[DMR07] Digne, F., Michel, J. and Rouquier, R., Cohomologie des variétés de Deligne– Lusztig. Adv. Math. 209 (2007), 749–822.Google Scholar

[DD93] Dipper, R. and Du, J., Harish-Chandra vertices. J. Reine Angew. Math. 437 (1993), 101–130.Google Scholar

[DD97] Dipper, R. and Du, J., Harish-Chandra vertices and Steinberg’s tensor product theorems for finite greneral linear groups. Proc. London Math. Soc. 75 (1997), 559–599.Google Scholar

[DF92] Dipper, R. and Fleischmann, P., Modular Harish-Chandra theory. I. Math. Z. 211 (1992), 49–71.Google Scholar

[Dr87] Drinfeld, V. G., Quantum groups. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), pp. 798–820, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

[DuMa18] Dudas, O. and Malle, G., Modular irreducibility of cuspidal unipotent characters. Invent. Math. 211 (2018), 579–589.Google Scholar

[Ef94] Eftekhari, M., Descente de Shintani des faisceaux caractères. C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), 305–308.Google Scholar

[En13] Enguehard, M., Towards a Jordan decomposition of blocks of finite reductive groups. Available at arxiv:1312.0106.Google Scholar

[EM17] Enguehard, M. and Michel, J., The Sylow subgroups of a finite reductive group. Bull. Inst. Math. Acad. Sinica 13 (2018), 227–247.Google Scholar

[Enn63] Ennola, V., On the characters of the finite unitary groups. Ann. Acad. Sci. Fenn. Ser. A I 323 (1963), 120–155.Google Scholar

[Eno72] Enomoto, H., The characters of the finite symplectic group Sp(4, q), q = 2^f . Osaka J. Math. 9 (1972), 75–94.Google Scholar

[Eno76] Enomoto, H., The characters of the finite Chevalley group G₂ (q), q = 3^f . Japan. J. Math. 2 (1976), 191–248.Google Scholar

[EnYa86] Enomoto, H. and Yamada, H., The characters of G₂ (2ⁿ). Japan. J. Math. 12 (1986), 325–377.Google Scholar

[Et11] Etingof, P., Golberg, O., Hensel, S., Liu, T., Schwendner, A., Vaintrob, D. and Yudovina, E., Introduction to Representation Theory. With Historical Interludes by Slava Gerovitch. Student Math. Library, vol. 59, Amer. Math. Soc., Providence, RI, 2011.Google Scholar

[Fei82] Feit, W., The Representation Theory of Finite Groups. North–Holland, Amsterdam, 1982.Google Scholar

[Fo69] Fogarty, J., Invariant Theory. W. A. Benjamin, New York, 1969.Google Scholar

[FoSr82] Fong, P. and Srinivasan, B., The blocks of finite general linear and unitary groups. Invent. Math. 69 (1982), 109–153.Google Scholar

[FoSr86] Fong, P. and Srinivasan, B., Generalized Harish-Chandra theory for unipotent characters of finite classical groups. J. Algebra 104 (1986), 301–309.Google Scholar

[FoSr89] Fong, P. and Srinivasan, B., The blocks of finite classical groups. J. Reine Angew. Math. 396 (1989), 122–191.Google Scholar

[FoSr90] Fong, P. and Srinivasan, B., Brauer trees in classical groups. J. Algebra 131 (1990), 179–225.Google Scholar

[Fro96] Frobenius, F. G., Über Gruppencharaktere. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin (1896), 985–1021.Google Scholar

[FuHa91] Fulton, W. and Harris, J., Representation Theory. A First Course. Graduate Texts in Mathematics, 129. Readings in Mathematics. Springer Verlag, New York, 1991.Google Scholar

[GAP4] The GAP Group, GAP – Groups, Algorithms, and Programming. Version 4.8.10, 2018. (www.gap-system.org)Google Scholar

[Ge92] Geck, M., On the classification of l-blocks of finite groups of Lie type. J. Algebra 151 (1992), 180–191.Google Scholar

[Ge93a] Geck, M., Basic sets of Brauer characters of finite groups of Lie type, II. J. London Math. Soc. (2) 47 (1993), 255–268.Google Scholar

[Ge93b] Geck, M., A note on Harish-Chandra induction. Manuscripta Math. 80 (1993), 393–401.Google Scholar

[Ge95] Geck, M., Beiträge zur Darstellungstheorie von Iwahori-Hecke-Algebren. Habilitationsschrift, Aachener Beiträge zur Mathematik 11, Verlag der Augustinus Buchhandlung, Aachen, 1995.Google Scholar

[Ge96] Geck, M., On the average values of the irreducible characters of finite groups of Lie type on geometric unipotent classes. Doc. Math. J. DMV 1 (1996), 293–317.Google Scholar

[Ge00] Geck, M., On the representation theory of Iwahori–Hecke algebras of extended finite Weyl groups. Represent. Theory 4 (2000), 370–397.Google Scholar

[Ge01] Geck, M., Modular Harish-Chandra series, Hecke algebras and (generalized) q-Schur algebras. Modular Representation Theory of Finite Groups (Charlottesville, VA, 1998), pp. 1–66, Walter de Gruyter, Berlin, 2001.Google Scholar

[Ge03a] Geck, M., An Introduction to Algebraic Geometry and Algebraic Groups. Oxford Graduate Texts in Mathematics, vol. 10, Oxford University Press, New York, 2003.CrossRefGoogle Scholar

[Ge03b] Geck, M., Character values, Schur indices and character sheaves. Represent. Theory 7 (2003), 19–55.Google Scholar

[Ge03c] Geck, M., On the Schur indices of cuspidal unipotent characters. Finite Groups 2003 (Gainesville, FL, 2003), pp. 87–104, Walter de Gruyter, Berlin, 2004.Google Scholar

[Ge03d] Geck, M., On the p-defects of character degrees of finite groups of Lie type. Carpathian J. Math. 19 (2003), 97–100.Google Scholar

[Ge05a] Geck, M., The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups E₇ (q). Osaka J. Math. 42 (2005), 201–215.Google Scholar

[Ge11] Geck, M., Some applications of CHEVIE to the theory of algebraic groups. Carpath. J. Math. 27 (2011), 64–94.Google Scholar

[Ge12a] Geck, M., Remarks on modular representations of finite groups of Lie type in non-defining characteristic. Algebraic Groups and Quantum Groups, pp. 71–80, Contemp. Math., 565, Amer. Math. Soc., Providence, RI, 2012.Google Scholar

[Ge12b] Geck, M., On the Kazhdan–Lusztig order on cells and families. Comment. Math. Helv. 87 (2012), 905–927.Google Scholar

[Ge13] Geck, M., On Kottwitz’ conjecture for twisted involutions. J. Lie Theory 25 (2015), 395–429.Google Scholar

[Ge17] Geck, M., On the construction of semisimple Lie algebras and Chevalley groups. Proc. Amer. Math. Soc. 145 (2017), 3233–3247.Google Scholar

[Ge18] Geck, M., A first guide to the character theory of finite groups of Lie type. Local Representation Theory and Simple Groups (eds. R. Kessar, G. Malle, D. Testerman), pp. 63–106, EMS Lecture Notes Series, EMS Publ. House, 2018.Google Scholar

[Ge19a] Geck, M., On the values of unipotent characters in bad characteristic. Rend. Cont. Sem. Mat. Univ. Padova 141 (2019), 37–63.Google Scholar

[Ge19b] Geck, M., Green functions and Glauberman degree-divisibility. See arXiv: 1904.04586.Google Scholar

[Ge19c] Geck, M., Computing Green functions in small characteristic. J. Algebra (2020), to appear.Google Scholar

[GeHe08] Geck, M. and Hézard, D., On the unipotent support of character sheaves. Osaka J. Math. 45 (2008), 819–831.Google Scholar

[GeHi91] Geck, M. and Hiss, G., Basic sets of Brauer characters of finite groups of Lie type. J. Reine Angew. Math. 418 (1991), 173–188.Google Scholar

[GeHi97] Geck, M. and Hiss, G., Modular representations of finite groups of Lie type in non-defining characteristic. Finite Reductive Groups: Related Structures and Representations (Luminy, 1994), pp. 195–249, Birkhäuser Boston, Ma, 1997.Google Scholar

[GHLMP] Geck, M., Hiß, G., Lübeck, F., Malle, G. and Pfeiffer, G., CHEVIE–A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras. Appl. Algebra Engrg. Comm. Comput. 7 (1996), 175–210; see also www.math.rwth-aachen.de/~CHEVIE.Google Scholar

[GHM94] Geck, M., Hiss, G. and Malle, G., Cuspidal unipotent Brauer characters. J. Algebra 168 (1994), 182–220.Google Scholar

[GHM96] Geck, M., Hiss, G. and Malle, G., Towards a classification of the irreducible representations in non-describing characteristic of a finite group of Lie type. Math. Z. 221 (1996), 353–386.Google Scholar

[GeIa12] Geck, M. and Iancu, L., Ordering Lusztig’s families in type B_n. J. Algebraic Comb. 38 (2013), 457–489.Google Scholar

[GIM00] Geck, M., Iancu, L. and Malle, G., Weights of Markov traces and generic degrees. Indag. Math. (N.S.) 11 (2000), 379–397.Google Scholar

[GeJa11] Geck, M. and Jacon, N., Representations of Hecke Algebras at Roots of Unity. Algebra and Applications, vol. 15, Springer-Verlag, London, 2011.Google Scholar

[GKP00] Geck, M., Kim, S. and Pfeiffer, G., Minimal length elements in twisted conjugacy classes of finite Coxeter groups. J. Algebra 229 (2000), 570–600.Google Scholar

[GeMa99] Geck, M. and Malle, G., On special pieces in the unipotent variety. Experiment. Math. 8 (1999), 281–290.Google Scholar

[GeMa00] Geck, M. and Malle, G., On the existence of a unipotent support for the irreducible characters of finite groups of Lie type. Trans. Amer. Math. Soc. 352 (2000), 429–456.Google Scholar

[GeMa03] Geck, M. and Malle, G., Fourier transforms and Frobenius eigenvalues for finite Coxeter groups. J. Algebra 260 (2003), 162–193.Google Scholar

[GePf92] Geck, M. and Pfeiffer, G., The unipotent characters of the Chevalley groups D₄ (q), q odd. Manuscripta Math. 76 (1992), 281–304.CrossRefGoogle Scholar

[GePf00] Geck, M. and Pfeiffer, G., Characters of Finite Coxeter Groups and Iwahori– Hecke Algebras. London Mathematical Society Monographs. New Series, 21. The Clarendon Press, Oxford University Press, New York, 2000.Google Scholar

[GoWa98] Goodman, R. and Wallach, N. R., Symmetry, Representations and Invariants. Graduate Texts in Mathematics vol. 255, Springer Verlag, Berlin–Heidelberg– New York, 2009.Google Scholar

[GLS94] Gorenstein, D., Lyons, R. and Solomon, R., The Classification of the Finite Simple Groups. Math. Surveys and Monographs vol. 40, no. 1, Amer. Math. Soc., 1994.Google Scholar

[GLS96] Gorenstein, D., Lyons, R. and Solomon, R., The Classification of the Finite Simple Groups. Math. Surveys and Monographs vol. 40, no. 2, Amer. Math. Soc., 1996.Google Scholar

[GLS98] Gorenstein, D., Lyons, R. and Solomon, R., The Classification of the Finite Simple Groups. Math. Surveys and Monographs vol. 40, no. 3, Amer. Math. Soc., 1998.Google Scholar

[Gre55] Green, J. A., The characters of the finite general linear groups. Trans. Amer. Math. Soc. 80 (1955), 402–447.Google Scholar

[Gre99] Green, J. A., Discrete series characters for GL(n, q). Algebr. Represent. Theory 2 (1999), 61–82.Google Scholar

[Gro02] Grove, L. C., Classical Groups and Geometric Algebra. Graduate Studies in Math., vol. 39, Amer. Math. Soc., Providence, RI, 2002.Google Scholar

[GM12a] Guralnick, R. M. and Malle, G., Products of conjugacy classes and fixed point spaces. J. Amer. Math. Soc. 25 (2012), 77–121.Google Scholar

[GM12b] Guralnick, R. M. and Malle, G., Simple groups admit Beauville structures. J. London Math. Soc. 85 (2012), 694–721.Google Scholar

[GMT13] Guralnick, R. M., Malle, G. and Tiep, P., Products of conjugacy classes in finite and algebraic simple groups. Adv. in Math. 234 (2013), 618–652.Google Scholar

[HaCh] Harish-Chandra, Eisenstein series over finite fields. Functional Analysis and Related Fields (Proc. Conf. M. Stone, Chicago, 1968), pp. 76–88, Springer, New York, 1970.Google Scholar

[He19] Hetz, J., On the values of unipotent characters of finite Chevalley groups of type E₆ in characteristic 3. J. Algebra 536 (2019), 242–255.Google Scholar

[Hi90a] Hiss, G., Regular and semisimple blocks of finite reductive groups. J. London Math. Soc. 41 (1990), 63–68.Google Scholar

[Hi90b] Hiss, G., Zerlegungszahlen endlicher Gruppen vom Lie-Typ in nicht-definierender Charakteristik. Habilitationsschrift, RWTH Aachen, 1990.Google Scholar

[Hi93] Hiss, G., Harish-Chandra series of Brauer characters in a finite group with a split BN-pair. J. London Math. Soc. 48 (1993), 219–228.Google Scholar

[Ho74] Hoefsmit, P., Representations of Hecke Algebras of Finite Groups with BN-Pairs of Classical Type. Ph. D. Thesis, The University of British Columbia (Canada), 1974.Google Scholar

[Ho19] Hollenbach, R., Quasi-Isolated Blocks and the Malle–Robinson Conjecture. Dissertation, TU Kaiserslautern, 2019.Google Scholar

[HoSh79] Hotta, R. and Shimomura, H., The fixed point subvarieties of unipotent transformations on generalized flag varieties and the Green functions. Math. Ann. 241 (1979), 193–208.Google Scholar

[HoSp77] Hotta, R. and Springer, T. A., A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups. Invent. Math. 41 (1977), 113–127.Google Scholar

[Ho80] Howlett, R. B., Normalizers of parabolic subgroups of reflection groups. J. London Math. Soc. (2) 21 (1980), 62–80.Google Scholar

[HoLe80] Howlett, R. B. and Lehrer, G. I., Induced cuspidal representations and generalised Hecke rings. Invent. Math. 58 (1980), 37–64.Google Scholar

[HoLe83] Howlett, R. B. and Lehrer, G. I., Representations of generic algebras and finite groups of Lie type. Trans. Amer. Math. Soc. 280 (1983), 753–779.Google Scholar

[HoLe94] Howlett, R. B. and Lehrer, G. I., On Harish-Chandra induction for modules of Levi subgroups. J. Algebra 165 (1994), 172–183.Google Scholar

[Hum91] Humphreys, J. E., Linear Algebraic Groups. Graduate Texts in Mathematics vol. 21, Springer Verlag, Berlin–Heidelberg–New York, 1975.Google Scholar

[Hum95] Humphreys, J. E., Conjugacy Classes in Semisimple Algebraic Groups. Math. Surveys and Monographs, vol. 43, Amer. Math. Soc., RI, 1995.Google Scholar

[Hup67] Huppert, B., Endliche Gruppen I. Grundlehren der math. Wissenschaften vol. 134, Springer, Heidelberg, 1967.Google Scholar

[HuBl82] Huppert, B. and Blackburn, N., Finite Groups II. Grundlehren der math. Wissenschaften vol. 242, Springer, Heidelberg, 1982.Google Scholar

[Ia01] Iancu, L., Markov traces and generic degrees in type B_n. J. Algebra 236 (2001), 731–744.Google Scholar

[Is76] Isaacs, I. M., Character Theory of Finite Groups. Academic Press, New York, 1976; corrected reprint by Dover Publ., New York, 1994.Google Scholar

[Iw64] Iwahori, N., On the structure of a Hecke ring of a Chevalley group over a finite field. J. Fac. Sci. Univ. Tokyo 10 (1964), 215–236.Google Scholar

[Ja86] James, G. D., The irreducible representations of the finite general linear groups. Proc. London Math. Soc. 52 (1986), 236–268.Google Scholar

[JaKe81] James, G. D. and Kerber, A., The Representation Theory of the Symmetric Group. Encyclopedia of Mathematics and its Applications, 16. Addison-Wesley Publishing Co., Reading, MA, 1981.Google Scholar

[Jan03] Jantzen, J. C., Representations of Algebraic Groups. Second edition. Mathematical Surveys and Monographs, 107. Amer. Math. Soc., Providence, RI, 2003.Google Scholar

[Jor07] Jordan, H., Group-characters of various types of linear groups. Amer. J. Math. 29 (1907), 387–405.Google Scholar

[Kac85] Kac, V., Infinite Dimensional Lie Algebras. Cambridge University Press, 1985.Google Scholar

[Kaw82] Kawanaka, N., Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field. Invent. Math. 69 (1982), 411–435.Google Scholar

[Kaw85] Kawanaka, N., Generalized Gel’fand-Graev representations and Ennola duality. Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), pp. 175–206, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985.Google Scholar

[Kaw86] Kawanaka, N., Generalized Gelfand-Graev representations of exceptional simple algebraic groups over a finite field I. Invent. Math. 84 (1986), 575–616.Google Scholar

[Kaw87] Kawanaka, N., Shintani lifting and Gel’fand-Graev representations. The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), pp. 147– 163, Proc. Sympos. Pure Math., vol. 47, Part 1, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

[Kaz77] Kazhdan, D. A., Proof of Springer’s hypothesis. Israel J. Math. 28 (1977), 272– 286.Google Scholar

[KaLu79] Kazhdan, D. A. and Lusztig, G., Representations of Coxeter groups and Hecke algebras. Invent. Math. 53 (1979), 165–184.Google Scholar

[KeMa13] Kessar, R. and Malle, G., Quasi-isolated blocks and Brauer’s height zero conjecture. Ann. of Math. (2) 178 (2013), 321–384.Google Scholar

[KeMa15] Kessar, R. and Malle, G., Lusztig induction and ℓ-blocks of finite reductive groups. Pacific J. Math. 279 (2015), 267–296.Google Scholar

[KeMa19] Kessar, R. and Malle, G., Characters in quasi-isolated blocks. In preparation.Google Scholar

[KlTi09] Kleshchev, A. and Tiep, P. H., Representations of finite special linear groups in non-defining characteristic. Adv. Math. 220 (2009), 478–504.Google Scholar

[Klu16] Klupsch, M., On Cuspidal and Supercuspidal Representations of Finite Reductive Groups. Dissertation, RWTH Aachen University, 2016.Google Scholar

[Ko66] Kostant, B., Groups over Z. Algebraic Groups and Their Discontinuous Subgroups (Boulder, Colorado, 1965), pp. 90–98, Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc., Providence, RI, 1966.Google Scholar

[LaSr90] Lambe, L. and Srinivasan, B., A computation of Green functions for some classical groups. Comm. Algebra 18 (1990), 3507–3545.Google Scholar

[La56] Lang, S., Algebraic groups over finite fields. Amer. J. Math. 78 (1956), 555–563.Google Scholar

[Lau89] Laumon, G., Faisceaux caractères (d’après Lusztig). Séminaire Bourbaki, Vol. 1988/89. Astérisque No. 177–178 (1989), Exp. No. 709, 231–260.Google Scholar

[LLS14] Lawther, R., Liebeck, M. and Seitz, G., Outer unipotent classes in automorphism groups of simple algebraic groups. Proc. Lond. Math. Soc. (3) 109 (2014), 553– 595.Google Scholar

[Leh73] Lehrer, G. I., The characters of the finite special linear groups. J. Algebra 26 (1973), 564–583.Google Scholar

[Leh78] Lehrer, G. I., On the values of characters of semi-simple groups over finite fields. Osaka J. Math. 15 (1978), 77–99.Google Scholar

[LeSp99] Lehrer, G. I. and Springer, T., Intersection multiplicities and reflection subquotients of unitary reflection groups. I. Geometric Group Theory Down Under (Canberra, 1996), 181–193, de Gruyter, Berlin, 1999.Google Scholar

[LeSp99b] Lehrer, G. I. and Springer, T., Reflection subquotients of unitary reflection groups. Canad. J. Math. 51 (1999), 1175–1193.Google Scholar

[LeTa09] Lehrer, G. I. and Taylor, D. E., Unitary Reflection Groups. Australian Mathematical Society Lecture Series, 20. Cambridge University Press, 2009.Google Scholar

[LiSh05] Liebeck, M. and Shalev, A., Character degrees and random walks in finite groups of Lie type. Proc. London Math. Soc. 90 (2005), 61–86.Google Scholar

[Loc77] Locker, J., The complex irreducible characters of Sp(6, q), q even. Ph. D. Thesis, University of Sydney, 1977.Google Scholar

[Lue93] Lübeck, F., Charaktertafeln für die Gruppen CSp₆ (q) mit ungeradem q und Sp₆ (q) mit geradem q. Dissertation, Universität Heidelberg, 1993.Google Scholar

[Lue07] Lübeck, F., Data for finite groups of Lie type and related algebraic groups. See www.math.rwth-aachen.de/~Frank.Luebeck/chev/index.html.Google Scholar

[LM16] Lübeck, F. and Malle, G., A Murnaghan-Nakayama rule for values of unipotent characters in classical groups. Represent. Theory 20 (2016), 139–161; Corrigen-dum: ibid. 21 (2017), 1–3.Google Scholar

[Lu75] Lusztig, G., Sur la conjecture de Macdonald. C. R. Acad. Sci. Paris, Ser. A 280 (1975), 371–320.Google Scholar

[Lu76b] Lusztig, G., On the finiteness of the number of unipotent classes. Invent. Math. 34 (1976), 201–213.Google Scholar

[Lu76c] Lusztig, G., Coxeter orbits and eigenspaces of Frobenius. Invent. Math. 38 (1976), 101–159.Google Scholar

[Lu77a] Lusztig, G., Irreducible representations of finite classical groups. Invent. Math. 43 (1977), 125–175.Google Scholar

[Lu77b] Lusztig, G., Representations of Finite Chevalley Groups. C.B.M.S. Regional Conference Series in Mathematics, vol. 39, Amer. Math. Soc., Providence, RI, 1977.Google Scholar

[Lu79a] Lusztig, G., Unipotent representations of a finite Chevalley group of type E₈. Quart. J. Math. Oxford 30 (1979), 315–338.Google Scholar

[Lu79b] Lusztig, G., A class of irreducible representations of a finite Weyl group. Indag. Math. 41 (1979), 323–335.Google Scholar

[Lu80a] Lusztig, G., On the unipotent characters of the exceptional groups over finite fields. Invent. Math. 60 (1980), 173–192.Google Scholar

[Lu80b] Lusztig, G., Some problems in the representation theory of finite Chevalley groups. The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), pp. 313–317, Proc. Sympos. Pure Math. Vol. 37, Amer. Math. Soc., Providence, RI, 1980.Google Scholar

[Lu81a] Lusztig, G., On a theorem of Benson and Curtis. J. Algebra 71 (1981), 490–498.Google Scholar

[Lu81c] Lusztig, G., Unipotent characters of the symplectic and odd orthogonal groups over a finite field. Invent. Math. 64 (1981), 263–296.Google Scholar

[Lu82a] Lusztig, G., A class of irreducible representations of a finite Weyl group II. Indag. Math. 44 (1982), 219–226.Google Scholar

[Lu82b] Lusztig, G., Unipotent characters of the even orthogonal groups over a finite field. Trans. Amer. Math. Soc. 272 (1982), 733–751.Google Scholar

[Lu84a] Lusztig, G., Characters of Reductive Groups Over a Finite Field. Annals of Mathematics Studies, 107. Princeton University Press, Princeton, NJ, 1984.Google Scholar

[Lu84b] Lusztig, G., Characters of reductive groups over finite fields. Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), pp. 877– 880, PWN, Warsaw, 1984.Google Scholar

[Lu84c] Lusztig, G., Intersection cohomology complexes on a reductive group. Invent. Math. 75 (1984), 205–272.Google Scholar

[LuCS] Lusztig, G., Character sheaves. Adv. Math. 56 (1985), 193–237; II, 57 (1985), 226–265; III, 57 (1985), 266–315; IV, 59 (1986), 1–63; V, 61 (1986), 103–155.Google Scholar

[Lu86a] Lusztig, G., On the character values of finite Chevalley groups at unipotent elements. J. Algebra 104 (1986), 146–194.Google Scholar

[Lu87a] Lusztig, G., Introduction to character sheaves. The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), pp. 165–179, Proc. Symp. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

[Lu87b] Lusztig, G., Leading coefficients of character values of Hecke algebras. The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), pp. 235–262, Proc. Symp. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

[Lu88] Lusztig, G., On the representations of reductive groups with disconnected centre. Astérisque No. 168 (1988), 157–166.Google Scholar

[Lu89] Lusztig, G., Affine Hecke algebras and their graded versions. J. Amer. Math. Soc. 2 (1989), 599–635.Google Scholar

[Lu90] Lusztig, G., Green functions and character sheaves. Ann. of Math. (2) 131 (1990), 355–408.Google Scholar

[Lu91] Lusztig, G., Intersection cohomology methods in representation theory. Proceedings of the International Congress of Mathematics (Kyoto, 1990), pp. 155–174, Springer-Verlag, 1991.Google Scholar

[Lu92a] Lusztig, G., A unipotent support for irreducible representations. Adv. Math. 94 (1992), 139–179.Google Scholar

[Lu92b] Lusztig, G., Remarks on computing irreducible characters. J. Amer. Math. Soc. 5 (1992), 971–986.Google Scholar

[Lu93] Lusztig, G., Appendix: Coxeter groups and unipotent representations. Astérisque No. 212 (1993), 191–203.Google Scholar

[Lu94] Lusztig, G., Exotic Fourier transform. With an appendix by Gunter Malle. Duke Math. J. 73 (1994), 227–241, 243–248.Google Scholar

[Lu00] Lusztig, G., G(F_q)-invariants in irreducible G(F_q²)-modules. Represent. Theory 4 (2000), 446–465.Google Scholar

[Lu02] Lusztig, G., Rationality properties of unipotent representations. J. Algebra 258 (2002), 1–22.Google Scholar

[Lu03a] Lusztig, G., Homomorphisms of the alternating group A₅ into reductive groups. J. Algebra 260 (2003), 298–322.Google Scholar

[Lu03b] Lusztig, G., Hecke Algebras with Unequal Parameters. CRM Monographs Ser., vol. 18, Amer. Math. Soc., Providence, RI, 2003. Enlarged and updated version at arXiv:0208154v2.Google Scholar

[Lu04a] Lusztig, G., Character sheaves on disconnected groups. II. Represent. Theory 8 (2004), 72–124.Google Scholar

[Lu04b] Lusztig, G., Character sheaves on disconnected groups. IV. Represent. Theory 8 (2004), 145–178.Google Scholar

[Lu05] Lusztig, G., Unipotent elements in small characteristic. Transform. Groups 10 (2005), 449–487.Google Scholar

[Lu06] Lusztig, G., Character sheaves and generalizations. The Unity of Mathematics, pp. 443–455, Progr. Math. 244, Birkhäuser, Boston, 2006.Google Scholar

[Lu08a] Lusztig, G., Irreducible representations of finite spin groups. Represent. Theory 12 (2008), 1–36.Google Scholar

[Lu09a] Lusztig, G., Unipotent classes and special Weyl group representations. J. Algebra 321 (2009), 3418–3449.Google Scholar

[Lu09c] Lusztig, G., Study of a Z-form of the coordinate ring of a reductive group. J. Amer. Math. Soc. 22 (2009), 739–769.Google Scholar

[Lu09d] Lusztig, G., Twelve bridges from a reductive group to its Langlands dual. Representation Theory, pp. 125–143, Contemp. Math., 478, Amer. Math. Soc., Providence, RI, 2009.Google Scholar

[Lu09e] Lusztig, G., Character sheaves on disconnected groups. X. Represent. Theory 13 (2009), 82–140.Google Scholar

[Lu10] Lusztig, G., Bruhat Decomposition and Applications. Notes of a lecture at a one day conference in memory of F. Bruhat held at the Institut Poincaré, Paris; available at arXiv:1006.5004.Google Scholar

[Lu11] Lusztig, G., From conjugacy classes in the Weyl group to unipotent classes. Represent. Theory 15 (2011), 494–530.Google Scholar

[Lu12a] Lusztig, G., On the cleanness of cuspidal character sheaves. Mosc. Math. J. 12 (2012), 621–631.Google Scholar

[Lu12b] Lusztig, G., On the representations of disconnected reductive groups over F_q. Recent Developments in Lie Algebras, Groups and Representation Theory, ed. Misra, K., pp. 227–246, Proc. Symp. Pure Math. 86, Amer. Math. Soc., 2012.Google Scholar

[Lu13a] Lusztig, G., Families and Springer’s correspondence. Pacific J. Math. 267 (2014), 431–450.Google Scholar

[Lu14a] Lusztig, G., Restriction of a character sheaf to conjugacy classes. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 58 ( 106 ) (2015), 297–309.Google Scholar

[Lu14b] Lusztig, G., Unipotent representations as a categorical centre. Represent. Theory 19 (2015), 211–235.Google Scholar

[Lu14c] Lusztig, G., Algebraic and Geometric Methods in Representation Theory. Lecture at the Chinese University of Hong Kong, Sep. 25, 2014, arXiv:1409.8003.Google Scholar

[Lu16] Lusztig, G., Non-unipotent representations and categorical centres. Bull. Inst. Math. Acad. Sinica (N.S.) 12 (2017), 205–296.Google Scholar

[Lu17] Lusztig, G., Comments on my papers. See arXiv:1707.09368v3.Google Scholar

[Lu18a] Lusztig, G., On the definition of almost characters. Lie Groups, Geometry, and Representation Theory, ed. V. Kac et al., pp. 367–379, Progr. Math. 326, Birkhäuser, Boston, 2018.Google Scholar

[Lu18b] Lusztig, G., Special representations of Weyl groups: a positivity property. Adv. Math. 327 (2018), 161–172.Google Scholar

[Lu19] Lusztig, G., On the generalized Springer correspondence. Representations of Reductive Groups, pp. 219–253, Proc. Sympos. Pure Math., 101, Amer. Math. Soc., Providence, RI, 2019.Google Scholar

[LuSp79] Lusztig, G. and Spaltenstein, N., Induced unipotent classes. J. London Math. Soc. (2) 19 (1979), 41–52.Google Scholar

[LuSp85] Lusztig, G. and Spaltenstein, N., On the generalized Springer correspondence for classical groups. Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), pp. 289–316, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985.Google Scholar

[LuSr77] Lusztig, G. and Srinivasan, B., The characters of the finite unitary groups. J. Algebra 49 (1977), 167–171.Google Scholar

[LuYu19] Lusztig, G. and Yun, Z., Endoscopy for Hecke categories and character sheaves. See arXiv:1904.01176.Google Scholar

[LuPa10] Lux, K. and Pahlings, H., Representations of Groups. A Computational Approach. Cambridge Stud. Adv. Math., vol. 124. Cambridge University Press, 2010.Google Scholar

[Mac95] Macdonald, I. G., Symmetric Functions and Hall Polynomials. 2nd edition, Oxford University Press, 1995.Google Scholar

[Ma88] Malle, G., Exceptional groups of Lie type as Galois groups. J. Reine Angew. Math. 392 (1988), 70–109.Google Scholar

[Ma90] Malle, G., Die unipotenten Charaktere von ²F₄ (q₂). Comm. Algebra 18 (1990), 2361–2381.Google Scholar

[Ma90b] Malle, G., Some unitary groups as Galois groups over Q. J. Algebra 131 (1990), 476–482.Google Scholar

[Ma91] Malle, G., Darstellungstheoretische Methoden bei der Realisierung einfacher Gruppen vom Lie Typ als Galoisgruppen. Representation Theory of Finite Groups and Finite Dimensional Algebras, pp. 443–459, Progr. Math. 95, Birkhäuser, Basel, 1991.Google Scholar

[Ma93a] Malle, G., Generalized Deligne-Lusztig characters. J. Algebra 159 (1993), 64–97.Google Scholar

[Ma93b] Malle, G., Green functions for groups of types E₆ and F₄ in characteristic 2. Comm. Algebra 21 (1993), 747–798.Google Scholar

[Ma95] Malle, G., Unipotente Grade imprimitiver komplexer Spiegelungsgruppen. J. Algebra 177 (1995), 768–826.Google Scholar

[Ma97] Malle, G., Degrés relatifs des algèbres cyclotomiques associées aux groupes de réflexions complexes de dimension deux. Finite Reductive Groups: Related Structures and Representations (Luminy, 1994), pp. 311–332, Progr. Math. 141, Birkhäuser Boston, MA, 1997.Google Scholar

[Ma98] Malle, G., Spetses. Doc. Math., Extra Volume ICM II (1998), 87–96.Google Scholar

[Ma99] Malle, G., On the rationality and fake degrees of characters of cyclotomic algebras. J. Math. Sci. Univ. Tokyo 6 (1999), 647–677.Google Scholar

[Ma00] Malle, G., On the generic degrees of cyclotomic algebras. Represent. Theory 4 (2000), 342–369.Google Scholar

[Ma05] Malle, G., Springer correspondence for disconnected exceptional groups. Bull. London Math. Soc. 37 (2005), 391–398.Google Scholar

[Ma07] Malle, G., Height 0 characters of finite groups of Lie type. Represent. Theory 11 (2007), 192–220.Google Scholar

[Ma08] Malle, G., Extensions of unipotent characters and the inductive McKay condition. J. Algebra 320 (2008), 2963–2980.Google Scholar

[Ma14] Malle, G., The proof of Ore’s conjecture [after Ellers–Gordeev and Liebeck– O’Brien–Shalev–Tiep]. Sém. Bourbaki, Astérisque No. 361 (2014), Exp. 1069, 325–348.Google Scholar

[Ma17] Malle, G., Local-global conjectures in the representation theory of finite groups. Representation Theory — Current Trends and Perspectives, pp. 519–539, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2017.Google Scholar

[Ma17b] Malle, G., Cuspidal characters and automorphisms. Adv. Math. 320 (2017), 887–903.Google Scholar

[MaMa18] Malle, G. and Matzat, B. H., Inverse Galois Theory. 2nd edition. Springer, Berlin, 2018.Google Scholar

[MaRo03] Malle, G. and Rouquier, R., Familles de caractères de groupes de réflexions complexes. Represent. Theory 7 (2003), 610–640.Google Scholar

[MSW94] Malle, G., Saxl, J. and Weigel, T., Generation of classical groups. Geom. Dedicata 49 (1994), 85–116.Google Scholar

[MaSo04] Malle, G. and Sorlin, K., Springer correspondence for disconnected groups. Math. Z. 246 (2004), 291–319.Google Scholar

[MaTe11] Malle, G. and Testerman, D., Linear Algebraic Groups and Finite Groups of Lie Type. Cambridge Studies in Advanced Mathematics, 133. Cambridge University Press, 2011.Google Scholar

[MZ01] Malle, G. and Zalesskii, A. E., Prime power degree representations of quasi-simple groups. Archiv Math. 77 (2001), 461–468.Google Scholar

[MaSp89] Mars, J. G. M. and Springer, T. A., Character sheaves. Orbites Unipotentes et Représentations, III. Astérisque No. 173–174 (1989), 111–198.Google Scholar

[Mas10] Maslowski, J., Equivariant Character Bijections in Groups of Lie Type. Dissertation, Technische Universität Kaiserslautern, 2010. Available at https: //kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2229.Google Scholar

[Mat04] Mathas, A., Matrix units and generic degrees for the Ariki-Koike algebras. J. Algebra 281 (2004), 695–730.Google Scholar

[MiChv] Michel, J., The development version of the CHEVIE package of GAP3. J. Algebra 435 (2015), 308–336. See also http://people.math.jussieu.fr/~jmichel/chevie/chevie.html.Google Scholar

[Miz77] Mizuno, K., The conjugate classes of Chevalley groups of type E₆. J. Fac. Sci. Univ. Tokyo 24 (1977), 525–563.Google Scholar

[Miz80] Mizuno, K., The conjugate classes of unipotent elements of the Chevalley groups E₇ and E₈. Tokyo J. Math. 3 (1980), 391–461.Google Scholar

[Mor63] Morris, A. O., The characters of the group GL(n, q). Math. Z. 81 (1963), 112–123.Google Scholar

[Mu03] Müller, P., Algebraic groups over finite fields, a quick proof of Lang’s theorem. Proc. Amer. Math. Soc. 131 (2003), 369–370.Google Scholar

[Na18] Navarro, G., Character Theory and the McKay Conjecture. Cambridge Studies in Advanced Mathematics, 175. Cambridge University Press, 2018.Google Scholar

[Na19] Navarro, G., On a question of C. Bonnafé on characters and multiplicity free constituents. J. Algebra 520 (2019), 517–519.Google Scholar

[Ohm77] Ohmori, Z., On the Schur indices of GL(n, q) and SL(2n + 1, q). J. Math. Soc. Japan 29 (1977), 693–707.Google Scholar

[Ohm96] Ohmori, Z., The Schur indices of the cuspidal unipotent characters of the finite unitary groups. Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), 111–113.Google Scholar

[Ol84] Olsson, J. B., Remarks on symbols, hooks and degrees of unipotent characters. J. Combin. Theory Ser. A 42 (1986), 223–238.Google Scholar

[Op95] Opdam, E., A remark on the irreducible characters and fake degrees of finite real reflection groups. Invent. Math. 120 (1995), 447–454.Google Scholar

[OrTe92] Orlik, P. and Terao, H., Arrangements of Hyperplanes. Grundlehren der Mathematischen Wissenschaften, 300. Springer-Verlag, Berlin, 1992.Google Scholar

[Os54] Osima, M., On the representations of the generalized symmetric group. Math. J. Okayama Univ. 4 (1954), 39–56.Google Scholar

[PaVi10] Panyushev, D. I. and Vinberg, E. B., The work of Vladimir Morozov on Lie algebras. Transform. Groups 15 (2010), 1001–1013.Google Scholar

[Pr82] Przygocky, A., Schur indices of symplectic groups. Comm. Algebra 10 (1982), 279–310.Google Scholar

[Re07] Reeder, M., On the restriction of Deligne-Lusztig characters. J. Amer. Math. Soc. 20 (2007), 573–602.Google Scholar

[Rou08] Rouquier, R., q-Schur algebras and complex reflection groups. Mosc. Math. J. 8 (2008), 119–158.Google Scholar

[Ru01] Rui, H., Weights of Markov traces on cyclotomic Hecke algebras. J. Algebra 238 (2001), 762–775.Google Scholar

[Sa71] Satake, I., Classification Theory of Semi-Simple Algebraic Groups. With an appendix by M. Sugiura. Lecture Notes in Pure and Applied Mathematics, 3. Marcel Dekker, Inc., New York, 1971.Google Scholar

[Sche85] Schewe, K. D., Blöcke exzeptioneller Chevalley-Gruppen. Bonner Mathematische Schriften 165, Universität Bonn, Math. Institut, 1985.Google Scholar

[Scho97] Schönert, M. et. al., GAP – Groups, algorithms, and programming – version 3 release 4 patchlevel 4. Lehrstuhl D für Mathematik, RWTH Aachen, Germany, 1997.Google Scholar

[Schu07] Schur, I., Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen. J. Reine Angew. Math. 132 (1907), 85–137.Google Scholar

[ST54] Shephard, G. C. and Todd, J. A., Finite unitary reflection groups. Canadian J. Math. 6 (1954), 274–304.Google Scholar

[Shi75] Shinoda, K., The conjugacy classes of the finite Ree groups of type (F₄ ). J. Fac. Sci. Univ. Tokyo 22 (1975), 1–15.Google Scholar

[Shi82] Shinoda, K., The characters of the finite conformal symplectic group CSp(4, q). Comm. Algebra 10 (1982), 1369–1419.Google Scholar

[Shi76] Shintani, T., Two remarks on irreducible characters of finite general linear groups. J. Math. Soc. Japan 28 (1976), 396–414.Google Scholar

[Sho82] Shoji, T., On the Green polynomials of a Chevalley group of type F₄. Comm. Algebra 10 (1982), 505–543.Google Scholar

[Sho83] Shoji, T., On the Green polynomials of classical groups. Invent. Math. 74 (1983), 239–267.Google Scholar

[Sho85] Shoji, T., Some generalization of Asai’s result for classical groups. Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), pp. 207–229, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985.Google Scholar

[Sho87] Shoji, T., Shintani descent for exceptional groups over a finite field. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), 599–653.Google Scholar

[Sho86] Shoji, T., Green functions of reductive groups over a finite field. The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986), pp. 289– 302, Proc. Sympos. Pure Math., 47, Part 1, Amer. Math. Soc., Providence, RI, 1987.Google Scholar

[Sho88] Shoji, T., Geometry of orbits and Springer correspondence. Orbites Unipotentes et Représentations, I. Astérisque No. 168 (1988), 61–140.Google Scholar

[Sho95] Shoji, T., Character sheaves and almost characters of reductive groups, I, II. Adv. Math. 111 (1995), 244–313, 314–354.Google Scholar

[Sho96] Shoji, T., On the computation of unipotent characters of finite classical groups. Appl. Algebra Engrg. Comm. Comp. 7 (1996), 165–174.Google Scholar

[Sho97] Shoji, T., Unipotent characters of finite classical groups. Finite Reductive Groups: Related Structures and Representations (Luminy, 1994), pp. 373–413, Progr. Math. 141, Birkhäuser Boston, MA, 1997.Google Scholar

[Sho98] Shoji, T., Irreducible characters of finite Chevalley groups. Sugaku expositions 11 (1998), 19–37.Google Scholar

[Sho06a] Shoji, T., Lusztig’s conjecture for finite special linear groups. Represent. Theory 10 (2006), 164–222.Google Scholar

[Sho06b] Shoji, T., Generalized Green functions and unipotent classes for finite reductive groups. I. Nagoya Math. J. 184 (2006), 155–198.Google Scholar

[Sho07] Shoji, T., Generalized Green functions and unipotent classes for finite reductive groups. II. Nagoya Math. J. 188 (2007), 133–170.Google Scholar

[Sho09] Shoji, T., Lusztig’s conjecture for finite classical groups with even characteristic. Representation Theory, pp. 207–236, Contemp. Math., 478, Amer. Math. Soc., Providence, RI, 2009.Google Scholar

[SiFr73] Simpson, W. A. and Frame, J. S., The character tables for SL(3, q), SU(3, q²), PSL(3, q) and PSU(3, q²). Canadian J. Math. 25 (1973), 486–494.Google Scholar

[So04] Sorlin, K., Springer correspondence in non connected reductive groups. J. Reine Angew. Math. 568 (2004), 197–234.Google Scholar

[Spa82a] Spaltenstein, N., Classes Unipotentes et Sous-Groupes de Borel. Lecture Notes in Mathematics, vol. 946, Springer, 1982.Google Scholar

[Spa82b] Spaltenstein, N., Charactères unipotents de ³D₄ (q³). Comment. Math. Helvetici 57 (1982), 676–691.Google Scholar

[Spa85] Spaltenstein, N., On the generalized Springer correspondence for exceptional groups. Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983), pp. 317– 338, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985.Google Scholar

[Spr70] Springer, T. A., Cusp forms for finite groups. Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69), pp. 97–120, Lecture Notes in Mathematics, Vol. 131 Springer, Berlin, 1970.Google Scholar

[Spr74] Springer, T. A., Regular elements of finite reflection groups. Invent. Math. 25 (1974), 159–198.Google Scholar

[Spr76] Springer, T. A., Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Invent. Math. 36 (1976), 173–207.Google Scholar

[Spr78] Springer, T. A., A construction of representations of Weyl groups. Invent. Math. 44 (1978), 279–293.Google Scholar

[Spr82] Springer, T. A., Quelques applications de la cohomologie d’intersection. Bourbaki Seminar, Vol. 1981/1982, pp. 249–273, Astérisque No. 92–93, Soc. Math. France, Paris, 1982Google Scholar

[Spr98] Springer, T. A., Linear Algebraic Groups. Second Edition, Progr. Math. 9, Birkhäuser, Boston, 1998.Google Scholar

[SpSt70] Springer, T. A. and Steinberg, R., Conjugacy classes. Seminar on Algebraic Groups and Related Finite Groups (The Institute for Advanced Study, Princeton, N.J., 1968/69), pp. 167–266, Lecture Notes in Mathematics, Vol. 131, Springer, Berlin, 1970.Google Scholar

[Sr68] Srinivasan, B., The characters of the finite symplectic group Sp(4, q). Trans. Amer. Math. Soc. 131 (1968), 488–525.Google Scholar

[Sr79] Srinivasan, B., Representations of Finite Chevalley Groups. Lecture Notes in Mathematics, vol. 764, Springer, 1979.Google Scholar

[Sr91] Srinivasan, B., Character sheaves: applications to finite groups. Algebraic Groups and Their Generalizations: Classical Methods (University Park, PA, 1991), pp. 183–194, Proc. Sympos. Pure Math., 56, Part 1, Amer. Math. Soc., Providence, RI, 1994.Google Scholar

[SrVi15] Srinivasan, B. and Vinroot, C. R., Jordan decomposition and real-valued characters of finite reductive groups with connected center. Bull. Lond. Math. Soc. 47 (2015), 427–435.Google Scholar

[SrVi18] Srinivasan, B. and Vinroot, C. R., Galois group action and Jordan decomposition of characters of finite reductive groups with connected center. J. Algebra, to appear.Google Scholar

[St51a] Steinberg, R., A geometric approach to the representations of the full linear group over a Galois field. Trans. Amer. Math. Soc. 71 (1951), 274–282. (See also [St97, pp. 1–9].)Google Scholar

[St51b] Steinberg, R., The representations of GL(3, q), GL(4, q), PGL(3, q), and PGL(4, q). Canadian J. Math. 3 (1951), 225–235. (See also [St97, pp. 11–21].)Google Scholar

[St57] Steinberg, R., Prime power representations of finite linear groups II. Canadian J. Math. 9 (1957), 347–351. (See also [St97, pp. 35–39].)Google Scholar

[St64] Steinberg, R., Differential equations invariant under finite reflection groups. Trans. Amer. Math. Soc. 112 (1964), 392–400.Google Scholar

[St67] Steinberg, R., Lectures on Chevalley groups. Mimeographed notes, Department of Math., Yale University, 1967. Now available as vol. 66 of the University Lecture Series, Amer. Math. Soc., Providence, RI, 2016.Google Scholar

[St68] Steinberg, R., Endomorphisms of Linear Algebraic Groups. Memoirs of the American Mathematical Society, No. 80 American Mathematical Society, Providence, RI, 1968. (See also [St97, pp. 229–285].)Google Scholar

[St74] Steinberg, R., Conjugacy Classes in Algebraic Groups. Notes by Vinay V. Deod-har. Lecture Notes in Mathematics, vol. 366. Springer-Verlag, Berlin–New York, 1974.Google Scholar

[St77] Steinberg, R., On theorems of Lie–Kolchin, Borel and Lang. Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, 349–354, Academic Press, New York, 1977. (See also [St97, pp. 467–472].)Google Scholar

[St97] Steinberg, R., Robert Steinberg. Collected Works, 7. American Mathematical Society, Providence, RI, 1997.Google Scholar

[St99] Steinberg, R., The isomorphism and isogeny theorems for reductive algebraic groups. Algebraic Groups and Their Representations (Cambridge, 1997), pp. 233–240, Kluwer Academic, Dordrecht, 1998.Google Scholar

[St99] Steinberg, R., The isomorphism and isogeny theorems for reductive algebraic groups. J. Algebra 216 (1999), 366–383.Google Scholar

[Su77] Surowski, D., Representations of a subalgebra of the generic algebra corresponding to the Weyl group of type F₄. Comm. Algebra 5 (1977), 873–888.Google Scholar

[Su78] Surowski, D., Degrees of irreducible characters of (B, N)-pairs of types E₆ and E₇. Trans. Amer. Math. Soc. 243 (1978), 235–249.Google Scholar

[Suz62] Suzuki, M., On a class of doubly transitive groups. Ann. of Math. 75 (1962), 105–145.Google Scholar

[Tay92] Taylor, D. E., The Geometry of Classical Groups. Sigma Series in Pure Math. vol. 9, Heldermann-Verlag, Berlin, 1992.Google Scholar

[Ta13] Taylor, J., On unipotent supports of reductive groups with a disconnected centre. J. Algebra 391 (2013), 41–61.Google Scholar

[Ta14b] Taylor, J., Evaluating characteristic functions of character sheaves at unipotent elements. Represent. Theory 18 (2014), 310–340.Google Scholar

[Ta16] Taylor, J., Generalised Gelfand–Graev representations in small characteristics. Nagoya Math. J. 224 (2016), 93–167.Google Scholar

[Ta18a] Taylor, J., On the Mackey formula for connected centre groups. J. Group Theory 21 (2018), 439–448.Google Scholar

[Ta18b] Taylor, J., Action of automorphisms on irreducible characters of symplectic groups. J. Algebra 505 (2018), 211–246.Google Scholar

[Ta19] Taylor, J., The structure of root data and smooth regular embeddings of reductive groups. Proc. Edinb. Math. Soc. 62 (2019), 523–552.Google Scholar

[TiZa04] Tiep, P. H. and Zalesskii, A. E., Unipotent elements of finite groups of Lie type and realization fields of their complex representations. J. Algebra 271 (2004), 327–390.Google Scholar

[Ti62] Tits, J., Théorème de Bruhat et sous-groupes paraboliques. C. R. Acad. Sci. Paris 254 (1962), 2910–2912.Google Scholar

[Vo07] Vogan, D., The character table for E₈. Notices Amer. Math. Soc. 54 (2007), 1122– 1134.Google Scholar

[Wal04] Waldspurger, J.-L., Une Conjecture de Lusztig Pour les Groupes Classiques. Mém. Soc. Math. France (N.S.), no. 96, 2004.Google Scholar

[War66] Ward, H. N., On Ree’s series of simple groups. Trans. Amer. Math. Soc. 121 (1966), 62–89.Google Scholar