Thursday 14th of December 2024, 13:30-14:30 in HG03.082
Stein Meereboer
Quantization of Semisimple Lie Algebras.
You have been lied to your whole life; quantum groups are not even groups at all. Or are they? We will find out. In the talk, we will take a pedestrian approach to Drinfel'd-Jimbo quantum groups. This special class of quantum groups originated around the 80s in the solution of the quantum Yang-Baxter equation in 2-dimensional statistical mechanics. In particular, we will construct the quantum group \(U_q(\mathfrak{sl}_2)\), which is an example of a quantized semisimple Lie algebra. We will motivate the construction, and during this journey, I want to point out certain choices one could make in the analytic approach. If time permits, we will look at the representation theory of \(U_q(\mathfrak{sl}_2)\), which may look quite familiar to some of you.