Representations of Quantum Conjugacy Classes of Orthosymplectic Groups

Abstract

Let G be the complex symplectic or special orthogonal group and let ɡ be 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(ɡ) 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 supports different representations of the same quantum conjugacy class. Bibliography: 25 titles.