Hecke category actions via Smith-Treumann theory

Abstract

Let $\text{G}$ 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 ${\text{Rep}}_0(\text{G})$ of $\text{Rep}(\text{G})$ by wall-crossing functors. This action was conjectured to exist by Riche-Williamson. Our method uses constructible sheaves and relies on Smith-Treumann theory.

38 pages, preliminary version