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.
Categories: math.RT