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SIGMA, 2010, Volume 6, 010, 13 pages (Mi sigma467)  

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

DOI: https://doi.org/10.3842/SIGMA.2010.010

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Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/010/
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Bibliographic databases:

ArXiv: 0912.5403
MSC: 17B37; 81R50
Received: November 5, 2009; in final form January 15, 2010; Published online January 26, 2010
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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.

Citation in format AMSBIB
\Bibitem{AshBurHav10}
\by Raisa M.~Asherova, {\v C}estm{\'\i}r Burd{\'\i}k, Miloslav Havl{\'\i}{\v{c}}ek, Yuri F.~Smirnov, Valeriy N.~Tolstoy
\paper $q$-Analog of Gelfand--Graev Basis for the Noncompact Quantum Algebra $U_q(u(n,1))$
\jour SIGMA
\yr 2010
\vol 6
\papernumber 010
\totalpages 13
\mathnet{http://mi.mathnet.ru/sigma467}
\crossref{https://doi.org/10.3842/SIGMA.2010.010}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2593372}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896062041}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tolstoy V.N., “Extremal projectors for contragredient Lie (super)symmetries (short review)”, Phys Atomic Nuclei, 74:12 (2011), 1747–1757  crossref  adsnasa  isi  elib  scopus
    2. Mudrov A., “Orthogonal Basis For the Shapovalov Form on U-Q (Sl(N+1))”, Rev. Math. Phys., 27:2 (2015), 1550004  crossref  mathscinet  zmath  isi  elib  scopus
    3. Ashton T., Mudrov A., “R-Matrix and Mickelsson Algebras For Orthosymplectic Quantum Groups”, J. Math. Phys., 56:8 (2015), 081701  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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