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Presenting generalized $q$-Schur algebras

Author(s): Stephen Doty
Journal: Represent. Theory 7 (2003), 196-213.
MSC (2000): Primary 17B37, 16W35, 81R50
Posted: May 20, 2003
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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: 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
Posted: May 20, 2003
Copyright of article: Copyright 2003, American Mathematical Society

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