Embeddings of the Racah Algebra into the Bannai-Ito Algebra
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also...
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| Дата: | 2015 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2015
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147119 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Embeddings of the Racah Algebra into the Bannai-Ito Algebra / V.X. Genest, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147119 |
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dspace |
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irk-123456789-1471192019-02-14T01:23:46Z Embeddings of the Racah Algebra into the Bannai-Ito Algebra Genest, V.X. Vinet, L. Zhedanov, A. Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also seen to hold independently of the realization. Second, the relationship between the realizations of the Bannai-Ito and Racah algebras by the intermediate Casimir operators of the osp(1|2) and su(1,1) Racah problems is established. Equivalently, this gives an embedding of the invariance algebra of the generic superintegrable system on the two-sphere into the invariance algebra of its extension with reflections, which are respectively isomorphic to the Racah and Bannai-Ito algebras. 2015 Article Embeddings of the Racah Algebra into the Bannai-Ito Algebra / V.X. Genest, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C80 DOI:10.3842/SIGMA.2015.050 http://dspace.nbuv.gov.ua/handle/123456789/147119 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Embeddings of the Racah algebra into the Bannai-Ito algebra are proposed in two realizations. First, quadratic combinations of the Bannai-Ito algebra generators in their standard realization on the space of polynomials are seen to generate a central extension of the Racah algebra. The result is also seen to hold independently of the realization. Second, the relationship between the realizations of the Bannai-Ito and Racah algebras by the intermediate Casimir operators of the osp(1|2) and su(1,1) Racah problems is established. Equivalently, this gives an embedding of the invariance algebra of the generic superintegrable system on the two-sphere into the invariance algebra of its extension with reflections, which are respectively isomorphic to the Racah and Bannai-Ito algebras. |
| format |
Article |
| author |
Genest, V.X. Vinet, L. Zhedanov, A. |
| spellingShingle |
Genest, V.X. Vinet, L. Zhedanov, A. Embeddings of the Racah Algebra into the Bannai-Ito Algebra Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Genest, V.X. Vinet, L. Zhedanov, A. |
| author_sort |
Genest, V.X. |
| title |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra |
| title_short |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra |
| title_full |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra |
| title_fullStr |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra |
| title_full_unstemmed |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra |
| title_sort |
embeddings of the racah algebra into the bannai-ito algebra |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147119 |
| citation_txt |
Embeddings of the Racah Algebra into the Bannai-Ito Algebra / V.X. Genest, L. Vinet, A. Zhedanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 20 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-11T01:23:59Z |
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2025-07-11T01:23:59Z |
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