Kenny De Commer

Quantizing real semisimple Lie groups

Let $\mathfrak g$ be a semisimple complex Lie algebra with compact real form $\mathfrak u$. The real forms of $\mathfrak g$ are in one-to-one connection with the Lie algebra involutions of $\mathfrak u$, which in turn are determined by the inclusion of their associated fixed point subalgebra $\mathfrak k$ in $\mathfrak u$. The latter inclusions are called compact symmetric pairs, and work of (among others) Noumi, Letzter and Kolb has shown that they admit quantizations as coideal subalgebras of Drinfeld-Jimbo quantized enveloping algebras. This has led to a very rich theory with connections to topological quantum field theory and the categorification programme. In this talk, we will show how quantum symmetric pairs lead to a general theory of quantized semisimple real Lie groups. We illustrate the general theory with the particular case of quantum $SL(2,\mathbb{R})$. This is partly based on joint work with Joel Dzokou Talla.

XXXIX Workshop on Geometric Methods in Physics	19.06–25.06.2022
XI School on Geometry and Physics	27.06–1.07.2022

Event sponsored by:
University of Bialystok