q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1))
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 represent...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2010 |
| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2010
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146148 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862556684194414592 |
|---|---|
| author | Asherova, R.M. Burdík, Č. Havlíček, M. Smirnov, Y.F. Tolstoy, V.N. |
| author_facet | Asherova, R.M. Burdík, Č. Havlíček, M. Smirnov, Y.F. Tolstoy, V.N. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-25T22:33:36Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146148 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T22:33:36Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Asherova, R.M. Burdík, Č. Havlíček, M. Smirnov, Y.F. Tolstoy, V.N. 2019-02-07T19:04:36Z 2019-02-07T19:04:36Z 2010 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. 1815-0659 2010 Mathematics Subject Classification: 17B37; 81R50 https://nasplib.isofts.kiev.ua/handle/123456789/146148 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. 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 en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) Article published earlier |
| spellingShingle | q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) Asherova, R.M. Burdík, Č. Havlíček, M. Smirnov, Y.F. Tolstoy, V.N. |
| title | q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) |
| title_full | q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) |
| title_fullStr | q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) |
| title_full_unstemmed | q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) |
| title_short | q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra Uq(u(n,1)) |
| title_sort | q-analog of gelfand-graev basis for the noncompact quantum algebra uq(u(n,1)) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146148 |
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