Racah Polynomials and Recoupling Schemes of su(1,1)
The connection between the recoupling scheme of four copies of su(1,1), the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection coefficients between eigenfunctions separated in different spherical coordinate...
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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
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/123456789/147128 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Racah Polynomials and Recoupling Schemes of su(1,1) / S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147128 |
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irk-123456789-1471282019-02-14T01:24:07Z Racah Polynomials and Recoupling Schemes of su(1,1) Post, S. The connection between the recoupling scheme of four copies of su(1,1), the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection coefficients between eigenfunctions separated in different spherical coordinate systems and equivalently as different irreducible decompositions of the tensor product representations. As a consequence of the model, an extension of the quadratic algebra QR(3) is given. It is shown that this algebra closes only with the inclusion of an additional shift operator, beyond the eigenvalue operators for the bivariate Racah polynomials, whose polynomial eigenfunctions are determined. The duality between the variables and the degrees, and hence the bispectrality of the polynomials, is interpreted in terms of expansion coefficients of the separated solutions. 2015 Article Racah Polynomials and Recoupling Schemes of su(1,1) / S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 33D45; 33D80; 81R05; 81R12 DOI:10.3842/SIGMA.2015.057 http://dspace.nbuv.gov.ua/handle/123456789/147128 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 |
The connection between the recoupling scheme of four copies of su(1,1), the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection coefficients between eigenfunctions separated in different spherical coordinate systems and equivalently as different irreducible decompositions of the tensor product representations. As a consequence of the model, an extension of the quadratic algebra QR(3) is given. It is shown that this algebra closes only with the inclusion of an additional shift operator, beyond the eigenvalue operators for the bivariate Racah polynomials, whose polynomial eigenfunctions are determined. The duality between the variables and the degrees, and hence the bispectrality of the polynomials, is interpreted in terms of expansion coefficients of the separated solutions. |
| format |
Article |
| author |
Post, S. |
| spellingShingle |
Post, S. Racah Polynomials and Recoupling Schemes of su(1,1) Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Post, S. |
| author_sort |
Post, S. |
| title |
Racah Polynomials and Recoupling Schemes of su(1,1) |
| title_short |
Racah Polynomials and Recoupling Schemes of su(1,1) |
| title_full |
Racah Polynomials and Recoupling Schemes of su(1,1) |
| title_fullStr |
Racah Polynomials and Recoupling Schemes of su(1,1) |
| title_full_unstemmed |
Racah Polynomials and Recoupling Schemes of su(1,1) |
| title_sort |
racah polynomials and recoupling schemes of su(1,1) |
| publisher |
Інститут математики НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147128 |
| citation_txt |
Racah Polynomials and Recoupling Schemes of su(1,1) / S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 21 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT posts racahpolynomialsandrecouplingschemesofsu11 |
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2023-05-20T17:26:39Z |
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2023-05-20T17:26:39Z |
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