On representations of quantum conjugacy classes of GL(n)

Abstract

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.

17 pages, no figures

References in corpus (2)

• Non-Levi closed conjugacy classes of SP_q(2n)
• Quantum sphere S^4 as a non-Levi conjugacy class

Cited by in corpus (3)

• Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
• R-matrix and Mickelsson algebras for orthosymplectic quantum groups
• Quantization of borderline Levi conjugacy classes of orthogonal groups