On modular Soergel bimodules, Harish-Chandra bimodules, and category O

TL;DR

This paper advances the understanding of modular Harish-Chandra bimodules and category O by establishing localization theorems and connecting these categories to the affine Hecke category, extending prior foundational work.

Contribution

It proves a localization theorem for modular Harish-Chandra bimodules and category O, and links these categories to the affine Hecke category, building on previous research.

Findings

Established a modular version of the Bezrukavnikov-Mirkovic-Rumynin localization theorem.

Connected the category of Harish-Chandra bimodules to the affine Hecke category.

Extended the study of modular category O and bimodules in the modular setting.

Abstract

In this paper we continue the study of the category of modular Harish-Chandra bimodules initiated by Bezrukavnikov and Riche and also study the modular version of the BGG category $\mathcal{O}$. We prove a version of the Bezrukavnikov-Mirkovic-Rumynin localization theorem for the Harish-Chandra bimodules and for the category $\mathcal{O}$. We also relate the category of Harish-Chandra bimodules to the affine Hecke category building on the prior work of Bezrukavnikov and Riche.