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: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2023
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| 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862538619409924096 |
|---|---|
| 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.
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| first_indexed | 2026-03-12T18:12:20Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211876 |
| 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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