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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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Monomial Bases for q-Schur algebras
by
Jie Du
The University of New South Wales
Coauthors: Brian Parshall (University of Virginia)

We investigate q-Schur algebras as ``little quantum groups.'' Using the Beilinson-Lusztig-MacPherson construction of the quantized enveloping algebra of gln and its associated monomial basis, we easily give a presentation for the q-Schur algebra Sq(n, r). In turn, we obtain a new basis for the integral q-Schur algebra Sq(n, r) which consists of certain monomials in the original generators. Finally, when n >= r, we interpret the Hecke algebra part of the monomial basis for Sq(n, r) in terms of Kazhdan-Lusztig basis elements.

Date received: August 15, 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-03.