Quantum Harish-Chandra bimodules at roots of unity and affine Hecke category

Abstract

The category of Harish-Chandra bimodules for quantum groups was first appeared in the works about topological quantum field theory of surfaces. In this paper, we study this category when the quantum parameter q is an odd order root of unity. We relate the category to the category of affine Soergel bimodules and to non-commutative Springer resolution.