Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)
Quantum Algebra
2009-11-11 v1
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.
Keywords
Cite
@article{arxiv.math/0508169,
title = {Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)},
author = {D. Shklyarov and G. Zhang},
journal= {arXiv preprint arXiv:math/0508169},
year = {2009}
}
Comments
26 pages