Quantum Analogs of Tensor Product Representations of su(1,1)
We study representations of Uq(su(1,1)) that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra su(1,1). We determine the decomposition of these representations into irreducible *-representations of Uq(su(1,1)) by diagonalizing the action of t...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2011 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147402 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quantum Analogs of Tensor Product Representations of su(1,1) / W. Groenevelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862678697100705792 |
|---|---|
| author | Groenevelt, W. |
| author_facet | Groenevelt, W. |
| citation_txt | Quantum Analogs of Tensor Product Representations of su(1,1) / W. Groenevelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study representations of Uq(su(1,1)) that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra su(1,1). We determine the decomposition of these representations into irreducible *-representations of Uq(su(1,1)) by diagonalizing the action of the Casimir operator on suitable subspaces of the representation spaces. This leads to an interpretation of the big q-Jacobi polynomials and big q-Jacobi functions as quantum analogs of Clebsch-Gordan coefficients.
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| first_indexed | 2025-12-07T15:41:19Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147402 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:41:19Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Groenevelt, W. 2019-02-14T17:38:28Z 2019-02-14T17:38:28Z 2011 Quantum Analogs of Tensor Product Representations of su(1,1) / W. Groenevelt // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20G42; 33D80 DOI: http://dx.doi.org/10.3842/SIGMA.2011.077 https://nasplib.isofts.kiev.ua/handle/123456789/147402 We study representations of Uq(su(1,1)) that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra su(1,1). We determine the decomposition of these representations into irreducible *-representations of Uq(su(1,1)) by diagonalizing the action of the Casimir operator on suitable subspaces of the representation spaces. This leads to an interpretation of the big q-Jacobi polynomials and big q-Jacobi functions as quantum analogs of Clebsch-Gordan coefficients. This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quantum Analogs of Tensor Product Representations of su(1,1) Article published earlier |
| spellingShingle | Quantum Analogs of Tensor Product Representations of su(1,1) Groenevelt, W. |
| title | Quantum Analogs of Tensor Product Representations of su(1,1) |
| title_full | Quantum Analogs of Tensor Product Representations of su(1,1) |
| title_fullStr | Quantum Analogs of Tensor Product Representations of su(1,1) |
| title_full_unstemmed | Quantum Analogs of Tensor Product Representations of su(1,1) |
| title_short | Quantum Analogs of Tensor Product Representations of su(1,1) |
| title_sort | quantum analogs of tensor product representations of su(1,1) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147402 |
| work_keys_str_mv | AT groeneveltw quantumanalogsoftensorproductrepresentationsofsu11 |