Semisimplicity of Hecke and (walled) Brauer algebras

Abstract

We show how to use Jantzen's sum formula for Weyl modules to prove semisimplicity criteria for endomorphism algebras of ${\text{U}}_q$-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 $\text{A}$ and $\text{B}$, the walled Brauer algebras and the Brauer algebras from our more general approach.

38 pages, lots of figures, revised version (e.g. added suggestions of a referee), to appear in J. Aust. Math. Soc., comments welcome

References in corpus (2)

• Blocks of cyclotomic Hecke algebras
• Diagram categories for ${\text{U}}_q$-tilting modules at roots of unity

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