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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2015 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2015
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147128 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862653934239219712 |
|---|---|
| author | Post, S. |
| author_facet | Post, S. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-01T23:49:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147128 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T23:49:28Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Post, S. 2019-02-13T17:10:27Z 2019-02-13T17:10:27Z 2015 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 https://nasplib.isofts.kiev.ua/handle/123456789/147128 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. 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.
 This manuscript is in honor of Luc Vinet in celebration of his 60th birthday. The author would
 like to thank the referees for their invaluable comments and suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Racah Polynomials and Recoupling Schemes of su(1,1) Article published earlier |
| spellingShingle | Racah Polynomials and Recoupling Schemes of su(1,1) Post, S. |
| title | 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_short | Racah Polynomials and Recoupling Schemes of su(1,1) |
| title_sort | racah polynomials and recoupling schemes of su(1,1) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147128 |
| work_keys_str_mv | AT posts racahpolynomialsandrecouplingschemesofsu11 |