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Representation Theory
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 ${\overset{\raisebox{-3pt}{$\boldsymbol.$ }}{\mathbf U}}$ of a quantized enveloping algebra. We show that generalized Schur algebras inherit a canonical basis from ${\overset{\raisebox{-3pt}{$\boldsymbol.$ }}{\mathbf 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
Email: doty@math.luc.edu

DOI: http://dx.doi.org/10.1090/S1088-4165-03-00176-6
PII: S 1088-4165(03)00176-6
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