Description
Braided monoidal categories are governed by braid groups of type A and the associated Yang-Baxter equation. Given a semisimple compact Lie group G, the Kazhdan-Lusztig theorem gives a non-trivial equivalence between two particular braided monoidal unitary categories: one constructed from a non-trivial associator on the category of unitary G-representations, using solutions to the so-called KZ-equation, and one constructed as the representation category of the quantization of G. In this talk, we will explain how the Kazhdan-Lusztig theorem has an analogue `in type B’, with quantum groups replaced by coideals and braided monoidal categories replaced by braided module categories, which are governed by braid groups of type B and the associated reflection equation. This is based on joint work with S. Neshveyev, L. Tuset and M. Yamashita.