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Australasian Research Symposium on Lie Groups, Algebraic Groups, Quantum Groups, and Their Representations (LAQ'2001)
December 7-10, 2001
The University of Auckland
Auckland, New Zealand

Organizers
Rod Gover (University of Auckland), Vladimir Pestov (Victoria University of Wellington)

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Tilting modules for cyclotomic Schur algebras.
by
Andrew Mathas
University of Sydney

The cyclotomic Schur algebras are endomorphism algebras of a direct sum of ``permutation like'' modules for the Ariki-Koike algebras: they include as special cases the q-Schur algebras of Dipper and James. These algebras were introduced partly to provide a new tool for studying the Ariki-Koike algebras and partly in the hope that they might generalize the beautiful Dipper-James theory which shows that the q-Schur algebras completely determine the modular representation theory of the GL_n(q) in non-defining characteristic. As yet there are no known (non type A) connections between the representation theory of the cyclotomic Schur algebras and that of the finite groups of Lie type; nonetheless the representation theory of these algebras is both rich and beautiful. For example, they are quasi-hereditary algebras and Jantzen's sum formula generalizes to this setting. In this talk I will survey the representation theory of the cyclotomic Schur algebras culminating with a description of their tilting modules.

http://www.maths.usyd.edu.au/u/mathas/

Date received: October 24, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahw-12.