Braided module categories provide a conceptual framework for the reflection equation, mimicking the relation between the Yang-Baxter equation and braided categories. Indeed, while the latter describes braids on a plane (type A
), the former can be thought of in terms of braids on a cylinder (type B
). In the theory of quantum groups, natural examples of braided module categories arise from quantum symmetric pairs (coideal subalgebras quantizing certain fixed point Lie subalgebra), where the action of type B
braid groups is given in terms of a so-called universal K
-matrix, constructed in finite-type by Balagovic-Kolb.
In this talk, I will describe the construction of a family of "parabolic” K
-matrices for quantum Kac-Moody algebras, which is indexed by Dynkin subdiagrams of finite-type and includes Balagovic-Kolb K
-matrix as a special case. If time permits, I will explain how this construction could lead to a meromorphic K
-matrix for quantum loop algebras.
This is based on joint works with D. Jordan and B. Vlaar.
the talk will be held in streaming, as a videoconference on-line; in order to join the videoconference, visit the web-page
and click on the link that you find there.