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arxiv 1507.07676 v3 pith:RQNS7MN6 submitted 2015-07-28 math.QA math.RAmath.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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On a symplectic quantum Howe duality

    math.RT 2023-03 unverdicted novelty 7.0

    Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.

  2. Sandwich cellularity and a version of cell theory

    math.RT 2022-06 unverdicted novelty 5.0

    Sandwich cellularity is presented as a version of cell theory for algebras and applied to Hecke algebras plus monoid and diagram algebras.

  3. Orthogonal webs and semisimplification

    math.RT 2024-01 unverdicted novelty 4.0

    A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.