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Representation Theory

ISSN 1088-4165



Presenting generalized $q$-Schur algebras

Author: Stephen Doty
Journal: Represent. Theory 7 (2003), 196-213
MSC (2000): Primary 17B37, 16W35, 81R50
Published electronically: May 20, 2003
MathSciNet review: 1990659
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Abstract: We obtain a presentation by generators and relations for generalized Schur algebras and their quantizations. This extends earlier results obtained in the type $A$ case. The presentation is compatible with Lusztig’s modified form $\mathbf {\dot {U}}$ of a quantized enveloping algebra. We show that generalized Schur algebras inherit a canonical basis from $\mathbf {\dot {U}}$, that this gives them a cellular structure, and thus they are quasihereditary over a field.

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Additional Information

Stephen Doty
Affiliation: Department of Mathematics and Statistics, Loyola University Chicago, Chicago, Illinois 60626
MR Author ID: 59395
ORCID: 0000-0003-3927-3009

Keywords: Schur algebras, $q$-Schur algebras, generalized Schur algebras, quantized enveloping algebras
Received by editor(s): August 31, 2002
Published electronically: May 20, 2003
Article copyright: © Copyright 2003 American Mathematical Society