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q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1))
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1))
Інший ID:
2010 Mathematics Subject Classification: 17B37; 81R50
Посилання:
q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) / R.M. Asherova // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 16 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the XVIIIth International Colloquium on Integrable Systems and Quantum Symmetries (June 18–20, 2009, Prague, Czech Republic). The full collection is available at http://www.emis.de/journals/SIGMA/ISQS2009.html.
The paper has been supported by grant RFBR-08-01-00392 (R.M.A., V.N.T.) and by grant
RFBR-09-01-93106-NCNIL-a (V.N.T.). The fifth author would like to thank Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague for hospitality
Дата:
2010
Переглядів:
731
Завантажень:
244
Анотація:
For the quantum algebra Uq(gl(n+1)) in its reduction on the subalgebra Uq(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Zq(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 noncompact quantum algebra Uq(u(n,1)) which is a real form of Uq(gl(n+1)), namely, an orthonormal Gelfand-Graev basis is constructed in an explicit form.
