An Askey-Wilson Algebra of Rank 2

An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra ((2, ℂ)). It is shown that bivariate -Racah...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2023
Hauptverfasser: Groenevelt, Wolter, Wagenaar, Carel
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2023
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211876
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:An Askey-Wilson Algebra of Rank 2. Wolter Groenevelt and Carel Wagenaar. SIGMA 19 (2023), 008, 35 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Groenevelt, Wolter
Wagenaar, Carel
author_facet Groenevelt, Wolter
Wagenaar, Carel
citation_txt An Askey-Wilson Algebra of Rank 2. Wolter Groenevelt and Carel Wagenaar. SIGMA 19 (2023), 008, 35 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra ((2, ℂ)). It is shown that bivariate -Racah polynomials appear as overlap coefficients of eigenvectors of generators of the algebra. Furthermore, the corresponding -difference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate -Racah polynomials.
first_indexed 2026-03-12T18:12:20Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2026-03-12T18:12:20Z
publishDate 2023
publisher Інститут математики НАН України
record_format dspace
spelling Groenevelt, Wolter
Wagenaar, Carel
2026-01-14T09:55:35Z
2023
An Askey-Wilson Algebra of Rank 2. Wolter Groenevelt and Carel Wagenaar. SIGMA 19 (2023), 008, 35 pages
1815-0659
2020 Mathematics Subject Classification: 20G42; 33D80
arXiv:2206.03986
https://nasplib.isofts.kiev.ua/handle/123456789/211876
https://doi.org/10.3842/SIGMA.2023.008
An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the quantum algebra ((2, ℂ)). It is shown that bivariate -Racah polynomials appear as overlap coefficients of eigenvectors of generators of the algebra. Furthermore, the corresponding -difference operators are calculated using the defining relations of the algebra, showing that it encodes the bispectral properties of the bivariate -Racah polynomials.
We thank the referees for their valuable suggestions, which helped to improve the paper.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
An Askey-Wilson Algebra of Rank 2
Article
published earlier
spellingShingle An Askey-Wilson Algebra of Rank 2
Groenevelt, Wolter
Wagenaar, Carel
title An Askey-Wilson Algebra of Rank 2
title_full An Askey-Wilson Algebra of Rank 2
title_fullStr An Askey-Wilson Algebra of Rank 2
title_full_unstemmed An Askey-Wilson Algebra of Rank 2
title_short An Askey-Wilson Algebra of Rank 2
title_sort askey-wilson algebra of rank 2
url https://nasplib.isofts.kiev.ua/handle/123456789/211876
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