Combinatorics of the center of the small quantum group

Abstract: The small quantum group $u_q(g)$ associated to the Lie algebra $g$ and a root of unity $q$ was introduced by Lusztig in 1990 and plays an important role in quantum and modular representation theory. Despite significant advances in the last two years, the dimension of the center of $u_q(g)$ is unknown in general. I will describe the combinatorial aspects of the problem, in particular the relation between the center of $u_q(g)$ and the space of the diagonal coinvariants, the Harish-Chandra center and the Higman ideal. This is a joint work with Qi You, Nicolas Hemelsoet and Oscar Kivinen.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home