We construct equivariant quantization of a special family of Levi conjugacy classes of the complex orthogonal group $SO(N)$, whose stabilizer contains a Cartesian factor $SO(2)\times SO(P)$, $1\leqslant P

Let G be the complex symplectic or special orthogonal group and g its Lie algebra.With every point x of the maximal torus T ⊂ 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. Mathematics Subject Classifications: 81R50, 81R60, 17B37.

Let g be a complex orthogonal or symplectic Lie algebra and g ′ ⊂ g the Lie subalgebra of rank rk g ′ = rk g − 1 of the same type. We give an explicit construction of generators of the Mickelsson algebra Z q (g, g ′ ) in terms of Chevalley generators via the R-matrix of U q (g).Mathematics Subject Classifications: 81R50, 81R60, 17B37.

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 ∈ O ∩ T we associate a highest weight module M a over the quantum group U q gl(n) and an equivariant quantization C ,a [O] of the polynomial ring C[O] realized by operators on M a . All quantizations C ,a [O] are isomorphic and can be regarded as different exact representations of the same algebra, C [O]. Similar results are obtained for semisimple adjoint orbits in gl(n) equipped with the canonical GL(n)-invariant Poisson structure. Mathematics Subject Classifications: 81R50, 81R60, 17B37.