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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2015 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2015
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147119 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862727285331722240 |
|---|---|
| author | Genest, V.X. Vinet, L. Zhedanov, A. |
| author_facet | Genest, V.X. Vinet, L. Zhedanov, A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T19:02:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147119 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:02:55Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Genest, V.X. Vinet, L. Zhedanov, A. 2019-02-13T16:58:46Z 2019-02-13T16:58:46Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147119 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. This paper is a contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of
 Luc Vinet. The full collection is available at http://www.emis.de/journals/SIGMA/ESSA2014.html.
 The authors would like to thank an anonymous referee for pointing out that the embedding of the
 Racah algebra in the Bannai–Ito algebra proposed in section two holds in the abstract. V.X.G. is
 supported by the Natural Science and Engineering Research Council of Canada (NSERC). The
 research of L.V. is supported in part by NSERC. A.Z. wishes to thank the Centre de Recherches
 Math´ematiques for its hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Embeddings of the Racah Algebra into the Bannai-Ito Algebra Article published earlier |
| spellingShingle | Embeddings of the Racah Algebra into the Bannai-Ito Algebra Genest, V.X. Vinet, L. Zhedanov, A. |
| title | 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_short | Embeddings of the Racah Algebra into the Bannai-Ito Algebra |
| title_sort | embeddings of the racah algebra into the bannai-ito algebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147119 |
| work_keys_str_mv | AT genestvx embeddingsoftheracahalgebraintothebannaiitoalgebra AT vinetl embeddingsoftheracahalgebraintothebannaiitoalgebra AT zhedanova embeddingsoftheracahalgebraintothebannaiitoalgebra |