Non-Levi closed conjugacy classes of SP_q(2n)

We construct explicit quantization of closed conjugacy classes of the complex symplectic group SP(2n) with non-Levi isotropy subgroups through an operator realization on highest weight modules over the quantum group U_q(sp(2n)).Comment: Replaced with the journal version. 38 page

On representations of quantum conjugacy classes of GL(n)

Let $O$ be a closed Poisson conjugacy class of the complex algebraic Poisson group GL(n) relative to the Drinfeld-Jimbo factorizable classical r-matrix. Denote by $T$ the maximal torus of diagonal matrices in GL(n). With every $a\in O\cap T$ we associate a highest weight module $M_a$ over the quantum group $U_q(gl(n))$ and an equivariant quantization $C_{h,a}[O]$ of the polynomial ring $C[O]$ realized by operators on $M_a$. All quantizations $C_{h,a}[O]$ are isomorphic and can be regarded as different exact representations of the same algebra, $C_{h}[O]$. Similar results are obtained for semisimple adjoint orbits in $gl(n)$ equipped with the canonical GL(n)-invariant Poisson structure.Comment: 17 pages, no figure

Representations of quantum conjugacy classes of orthosymplectic groups

Let $G$ be the complex symplectic or special orthogonal group and \g its Lie algebra. With every point $x$ of the maximal torus $T\subset G$ we associate a highest weight module $M_x$ over the Drinfeld-Jimbo quantum group U_q(\g) and a quantization of the conjugacy class of $x$ by operators in \End(M_x). These quantizations are isomorphic for $x$ lying on the same orbit of the Weyl group, and $M_x$ support different representations of the same quantum conjugacy class.Comment: 19 pages, no figure