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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Presenting generalized $q$-Schur algebras
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by Stephen Doty PDF
Represent. Theory 7 (2003), 196-213 Request permission

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.
References
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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
  • Email: doty@math.luc.edu
  • Received by editor(s): August 31, 2002
  • Published electronically: May 20, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 196-213
  • MSC (2000): Primary 17B37, 16W35, 81R50
  • DOI: https://doi.org/10.1090/S1088-4165-03-00176-6
  • MathSciNet review: 1990659