Hecke category actions via Smith-Treumann theory

2021/03/12 by Joshua Ciappara, Ciappara, Joshua · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2103.07091

openalex publication_date 2021/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 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 Rep₀(G) of Rep(G) by wall-crossing functors. This action was conjectured to exist by Riche-Williamson. Our method uses constructible sheaves and relies on Smith-Treumann theory.

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• Tilting modules for reductive algebraic groups: characters and support varieties

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