Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Parabolic K-matrices for quantum groups

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 the definition of a meromorphic K-matrix for quantum loop algebras. This is based on joint works with D. Jordan and B. Vlaar.