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

Quantum Conjugacy Classes of Simple Matrix Groups