Smith-Treumann theory and the linkage principle

Hecke category actions via Smith-Treumann theory

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

Steinberg商与Smith-Treumann局部化

Steinberg quotients and Smith-Treumann localization

本文通过涉及Steinberg模的卷积图，统一了仿射Grassmannian上的两种Smith-Treumann局部化，并将Steinberg商范畴化为仿射Grassmannian的Z/pZ不动点上球面奇偶层的茎。