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 $B_{c,s}$.

Substantial revision following referee comments; modified definition of the universal K-matrix to obtain a braided module category in all cases; added interpretation of the multiplicative behavior of the distinguished basis of the center in full generality; rewrote Section 3.4 to also hold in the Kac-Moody case; 33 pages, 6 figures

References in corpus (1)

• Canonical bases for tensor products and super Kazhdan-Lusztig theory

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