Universal K-matrix for quantum symmetric pairs
If you have a question about this talk, please contact David Craven.
Quantum groups provide a uniform setting for solutions of the quantum Yang-Baxter equation, which in turn leads to representations of the classical braid group in finitely many strands. Underlying this construction is the fact that the finite dimensional representations of a quantum group form a braided tensor category.
In a program to extend this construction to braid groups of type B, the topologist Tammo tom Dieck studied braids in a cylinder with one fixed axis. In the late 90s he introduced the notion of a braided tensor category with a cylinder twist which extends the categorical framework from type A to type B. However, only very few examples were known.
In this talk I will explain the above notions. I will then indicate how the theory of quantum symmetric pairs provides a large class of examples for tom Dieck’s theory. The construction builds on a program of canonical basis for quantum symmetric pairs initiated by H. Bao & W. Wang and related work by M. Ehrig & C. Stroppel. The new results in this talk are joint work with Martina Balagovic.
This talk is part of the Algebra Seminar series.
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