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arxiv: 1507.07676 · v3 · pith:RQNS7MN6new · submitted 2015-07-28 · 🧮 math.QA · math.RA· math.RT

Semisimplicity of Hecke and (walled) Brauer algebras

Henning Haahr Andersen , Catharina Stroppel , Daniel Tubbenhauer This is my paper
classification 🧮 math.QA math.RAmath.RT
keywords algebrasbrauersemisimplicitytextbfcriteriaheckemathbbmodules
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We show how to use Jantzen's sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of $\textbf{U}_q$-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 $\textbf{A}$ and $\textbf{B}$, the walled Brauer algebras and the Brauer algebras from our more general approach.

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