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20 April 2024

» arxiv » 0912.5403

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q-Analog of Gelfand--Graev basis for the noncompact quantum algebra U_q(u(n,1))
R.M. Asherova ; Č. Burdík ; M. Havlíček ; Yu.F. Smirnov ; V.N. Tolstoy ;
Date:	30 Dec 2009
Abstract:	For the quantum algebra U_{q}(gl(n+1)) in its reduction on the subalgebra U_{q}(gl(n)) an explicit description of a Mickelsson--Zhelobenko reduction Z-algebra Z_{q}(gl(n+1),gl(n)) is given in terms of the generators and their defining relations. Using this Z-algebra we describe Hermitian irreducible representations of a discrete series for the quantum algebra U_{q}(u(n,1)) which is a real form of U_{q}(gl(n+1)). Namely, an orthonormal Gelfand--Graev basis is constructed in explicit form.
Source:	arXiv, 0912.5403
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