Presenting generalized 𝑞-Schur algebras

Doty, Stephen

doi:10.1090/S1088-4165-03-00176-6

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.

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