Quantum conjugacy classes of simple matrix groups

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.

33 pages, AMS LaTeX

References in corpus (2)

• On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups
• Quantization of classical dynamical $r$-matrices with nonabelian base

Cited by in corpus (1)

• The GL(m|n) type quantum matrix algebras II: the structure of the characteristic subalgebra and its spectral parameterization