Quantum conjugacy classes of simple matrix groups

TL;DR

This paper constructs explicit quantum deformations of conjugacy classes in simple matrix groups, providing a detailed algebraic framework for their quantization with Levi subgroup stabilizers.

Contribution

It introduces a novel explicit method for quantizing conjugacy classes in simple matrix groups using Drinfeld-Jimbo quantum groups.

Findings

Explicit quantization formulas for conjugacy classes

Equivariant quantization respecting Levi subgroup stabilizers

Enhanced understanding of quantum group actions on conjugacy classes

Abstract

Let $G$ be a simple complex classical group and $\g$ its Lie algebra. Let $\U_\hbar(\g)$ be the Drinfeld-Jimbo quantization of the universal enveloping algebra $\U(\g)$. We construct an explicit $\U_\hbar(\g)$-equivariant quantization of conjugacy classes of $G$ with Levi subgroups as the stabilizers.