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This article is cited in 3 scientific papers (total in 3 papers)
$q$-Analog of Gelfand–Graev Basis for the Noncompact Quantum Algebra $U_q(u(n,1))$
Raisa M. Asherovaa, Čestmír Burdíkb, Miloslav Havlíčekb, Yuri F. Smirnova, Valeriy N. Tolstoyba a Institute of Nuclear Physics, Moscow State University, 119992 Moscow, Russia
b Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 12000 Prague 2, Czech Republic
Abstract:
For the quantum algebra $U_q(\mathfrak{gl}(n+1))$ in its reduction on the subalgebra $U_q(\mathfrak{gl}(n))$ $Z_q(\mathfrak{gl}(n+1),\mathfrak{gl}(n))$ 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 noncompact quantum algebra $U_q(u(n,1))$ which is a real form of $U_q(\mathfrak{gl}(n+1))$, namely, an orthonormal Gelfand–Graev basis is constructed in an explicit form.
Keywords:
quantum algebra; extremal projector; reduction algebra; Shapovalov form; noncompact quantum algebra; discrete series of representations; Gelfand–Graev basis.
Received: November 5, 2009; in final form January 15, 2010; Published online January 26, 2010
Citation:
Raisa M. Asherova, Čestmír Burdík, Miloslav Havlíček, Yuri F. Smirnov, Valeriy N. Tolstoy, “$q$-Analog of Gelfand–Graev Basis for the Noncompact Quantum Algebra $U_q(u(n,1))$”, SIGMA, 6 (2010), 010, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma467 https://www.mathnet.ru/eng/sigma/v6/p10
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