Mixed modular perverse sheaves on moment graphs

TL;DR

This paper introduces a new category of mixed modular perverse sheaves on moment graphs associated with Coxeter groups, generalizing graded category O and showing it is graded highest weight.

Contribution

It develops a novel Soergel-theoretic framework for mixed modular perverse sheaves on moment graphs linked to Coxeter groups, extending the theory of graded category O.

Findings

The category is graded highest weight.

Generalizes the theory of mixed modular derived categories.

Connects moment graph sheaves with graded category O.

Abstract

We study an analogue of the Achar-Riche "mixed modular derived category" for moment graphs. In particular, given a Coxeter group $W$ and a reflection faithful representation $\mathfrak{h}$, we introduce a category that plays the role of Schubert-stratified mixed modular perverse sheaves on "the flag variety associated to $(W, \mathfrak{h})$." We show that this Soergel-theoretic generalization of graded category $\mathcal{O}$ is graded highest weight.