Covariant q-differential operators and unitary highest weight representations for U{sub q}su{sub n,n}
Journal Article
·
· Journal of Mathematical Physics
- Department of Mathematics, Kansas State University, Manhattan, KS 66506 (United States)
We investigate a one-parameter family of quantum Harish-Chandra modules of U{sub q}sl{sub 2n}. This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U{sub q}su{sub 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.
- OSTI ID:
- 20699200
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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