Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra
The higher rank Askey-Wilson algebra was recently constructed in the n-fold tensor product of Uq(sl₂). In this paper, we prove a class of identities inside this algebra, which generalize the defining relations of the rank-one Askey-Wilson algebra. We extend the known construction algorithm by severa...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2019
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210289 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra / H. De Clercq // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862742305777123328 |
|---|---|
| author | De Clercq, H. |
| author_facet | De Clercq, H. |
| citation_txt | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra / H. De Clercq // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The higher rank Askey-Wilson algebra was recently constructed in the n-fold tensor product of Uq(sl₂). In this paper, we prove a class of identities inside this algebra, which generalize the defining relations of the rank-one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow for simplifying calculations significantly. At the same time, this provides proof of the corresponding relations for the higher rank q-Bannai-Ito algebra.
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| first_indexed | 2025-12-07T21:25:02Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210289 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:25:02Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | De Clercq, H. 2025-12-05T09:22:16Z 2019 Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra / H. De Clercq // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16T05; 16T15; 17B37; 81R50 arXiv: 1908.11654 https://nasplib.isofts.kiev.ua/handle/123456789/210289 https://doi.org/10.3842/SIGMA.2019.099 The higher rank Askey-Wilson algebra was recently constructed in the n-fold tensor product of Uq(sl₂). In this paper, we prove a class of identities inside this algebra, which generalize the defining relations of the rank-one Askey-Wilson algebra. We extend the known construction algorithm by several equivalent methods, using a novel coaction. These allow for simplifying calculations significantly. At the same time, this provides proof of the corresponding relations for the higher rank q-Bannai-Ito algebra. HDC is a PhD Fellow of the Research Foundation Flanders (FWO). This work was also supported by FWO Grant EOS 30889451. The author wishes to thank the anonymous referees for their valuable suggestions and comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra Article published earlier |
| spellingShingle | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra De Clercq, H. |
| title | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra |
| title_full | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra |
| title_fullStr | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra |
| title_full_unstemmed | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra |
| title_short | Higher Rank Relations for the Askey-Wilson and q-Bannai-Ito Algebra |
| title_sort | higher rank relations for the askey-wilson and q-bannai-ito algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210289 |
| work_keys_str_mv | AT declercqh higherrankrelationsfortheaskeywilsonandqbannaiitoalgebra |