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Cellular bases of generalised q-Schur algebras

  • STEPHEN DOTY (a1) and ANTHONY GIAQUINTO (a1)
Abstract
Abstract

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.

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[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).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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