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Hecke category actions via Smith–Treumann theory

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  23 August 2023

J. Ciappara
J. Ciappara*
Affiliation:
School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia joshua.ciappara@sydney.edu.au
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Abstract

Let $\textbf {G}$ be a simply connected semisimple algebraic group over a field of characteristic greater than the Coxeter number. We construct a monoidal action of the diagrammatic Hecke category on the principal block $\operatorname {Rep}_0(\textbf {G})$ of $\operatorname {Rep}(\textbf {G})$ by wall-crossing functors. This action was conjectured to exist by Riche and Williamson. Our method uses constructible sheaves and relies on Smith–Treumann theory.

Keywords

algebraic groupsrepresentationsconstructible sheavesHecke category

MSC classification

Primary: 20G05: Representation theory
Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 10 , October 2023 , pp. 2089 - 2124
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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