Representations of quantum conjugacy classes of orthosymplectic groups

Abstract

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