Skip to main content
    • Aa
    • Aa

Cellular bases of generalised q-Schur algebras


Starting from their defining presentation by generators and relations, we develop the basic structure and representation theory of generalised q-Schur algebras of finite type.

Hide All
[1] Beilinson A. A., Lusztig G. and MacPherson R.. A geometric setting for the quantum deformation of GL n . Duke Math. J. 61 (1990), 655677.
[2] Bourbaki N.. Algebra I, Chapters 1–3 (Translated from the French). Reprint of the 1989 English translation “Elements of Mathematics” (Berlin) (Springer–Verlag, Berlin, 1998).
[3] Chriss N. and Ginzburg V.. Representation Theory and Complex Geometry (Birkhäuser Boston 1997).
[4] Dipper R. and James G. D.. The q-Schur algebra. Proc. London Math. Soc. 59 (1989), 2350.
[5] Dipper R. and James G. D.. q-tensor space and q-Weyl modules. Trans. Amer. Math. Soc. 327 (1991), 251282.
[6] Donkin S.. On Schur algebras and related algebras I. J. Algebra 104 (1986), 310328.
[7] Donkin S.. On Schur algebras and related algebras II. J. Algebra 111 (1987), 354364.
[8] Donkin S.. On Schur algebras and related algebras III. integral representations. Math. Proc. Camb. Phil. Soc. 116 (1994), 3755.
[9] Doty S.. Presenting generalised q-Schur algebras. Represent. Theory 7 (2003), 196213 (electronic).
[10] Doty S.. Constructing quantised enveloping algebras via inverse limits of finite dimensional algebras. J. Algebra 321 (2009), 12251238.
[11] Doty S. and Giaquinto A.. Generators and relations for Schur algebras. Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 5462 (electronic).
[12] Doty S. and Giaquinto A.. Presenting Schur algebras. Internat. Math. Res. Not. 36 (2002), 19071944.
[13] Goodman F. and Graber J.. On cellular algebras with Jucys Murphy elements. J. Algebra 330 (2011), 147176.
[14] Graham J. J. and Lehrer G. I.. Cellular algebras. Invent. Math. 123 (1996), 134.
[15] Green J. A.. Polynomial representations of GL n , Lecture Notes in Math. 830. (Springer–Verlag, Berlin–New York, 1980), (Second edition 2007.)
[16] Humphreys J. E.. Introduction to Lie Algebras and Representation Theory (Springer 1972).
[17] Jantzen J. C.. Lectures on Quantum Groups. American Math. Soc. (1996).
[18] Jimbo M.. A q-analogue of inline-graphic $U(\mathfrak{gl}(N+1))$ , Hecke algebras and the Yang–Baxter equation. Lett. Math. Phys. 11 (1986), 247252.
[19] Kashiwara M., Miwa T., Petersen J.–U. H. and Yung C. M.. Perfect crystals and q-deformed Fock spaces. Selecta Math. (N.S.) 2 (1996), 415499.
[20] König S. and Xi C.. On the structure of cellular algebras. Algebras and modules, II (Geiranger, 1996) CMS Conf. Proc., 24 (Amer. Math. Soc., Providence, RI, 1998), 365386.
[21] König S. and Xi C.. Cellular algebras and quasi-hereditary algebras: a comparison. Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 7175 (electronic).
[22] Lusztig G.. Canonical bases in tensor products. Proc. Nat. Acad. Sci. U.S.A. 89 (1992), 81778179.
[23] Lusztig G.. Introduction to Quantum Groups (Birkhäuser, Boston 1993).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 26 *
Loading metrics...

Abstract views

Total abstract views: 92 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 21st October 2017. This data will be updated every 24 hours.