Covariant q-differential operators and unitary highest weight representations for U(q)su(n,)n
Journal article, 2005

We investigate a one-parameter family of quantum Harish-Chandra modules of Uq sl2n. This family is an analog of the holomorphic discrete series of representations of the group SU (n,n) for the quantum group Uq sun,n. We introduce a q -analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J. Faraut and A. Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series. © 2005 American Institute of Physics.


Dmitry Shklyarov

Kansas State University

Genkai Zhang

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Mathematical Physics

0022-2488 (ISSN) 1089-7658 (eISSN)

Vol. 46 6 24pp- 062307

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