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Hecke category actions via Smith–Treumann theory
Published online by Cambridge University Press: 23 August 2023
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.
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- Type
- Research Article
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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
References
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