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
Date:2011
Main Author: Groenevelt, W.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
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
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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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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
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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
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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
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