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Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

D. Shklyarov·G. Zhang
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Abstract

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, 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.

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BibTeXRIS

D. Shklyarov, G. Zhang. 2005-08-09. Covariant q-differential operators and unitary highest weight representations for U_q su(n,n). https://doi.org/10.1063/1.1927077

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