## Presenting generalized $q$-Schur algebras

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- by Stephen Doty
- Represent. Theory
**7**(2003), 196-213 - DOI: https://doi.org/10.1090/S1088-4165-03-00176-6
- Published electronically: 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 $\mathbf {\dot {U}}$ 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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*Internat. Math. Research Notices*, 2002:36 (2002), 1907-1944.

## Bibliographic 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