Braided module categories via quantum symmetric pairs

Abstract

Let ${\mathfrak g}$ be a finite dimensional complex semisimple Lie algebra. The finite dimensional representations of the quantized enveloping algebra $U_q({\mathfrak g})$ form a braided monoidal category $O_{int}$. We show that the category of finite dimensional representations of a quantum symmetric pair coideal subalgebra $B_{c,s}$ of $U_q({\mathfrak g})$ is a braided module category over an equivariantization of $O_{int}$. The braiding for $B_{c,s}$ is realized by a universal K-matrix which lies in a completion of $B_{c,s}\otimes U_q({\mathfrak g})$. We apply these results to describe a distinguished basis of the center of $B_{c,s}$.