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SEMISIMPLICITY OF HECKE AND (WALLED) BRAUER ALGEBRAS
Part of
- Lie algebras and Lie superalgebras
- Representation theory of groups
HENNING HAAHR ANDERSEN, CATHARINA STROPPEL, DANIEL TUBBENHAUER
Journal:

Journal of the Australian Mathematical Society / Volume 103 / Issue 1 / August 2017

Published online by Cambridge University Press:

25 October 2016, pp. 1-44

Print publication:

August 2017
- Article
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We show how to use Jantzen’s sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of $\mathbf{U}_{q}$-tilting modules (for any field $\mathbb{K}$ and any parameter $q\in \mathbb{K}-\{0,-1\}$). As an application, we recover the semisimplicity criteria for the Hecke algebras of types $\mathbf{A}$ and $\mathbf{B}$, the walled Brauer algebras and the Brauer algebras from our more general approach.