Mixed modular perverse sheaves on moment graphs

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.