The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1)
The 9j symbols of su(1,1) are studied within the framework of the generic superintegrable system on the 3-sphere. The canonical bases corresponding to the binary coupling schemes of four su(1,1) representations are constructed explicitly in terms of Jacobi polynomials and are seen to correspond to t...
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| Datum: | 2014 |
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| Sprache: | English |
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Інститут математики НАН України
2014
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146406 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) / Vincent X. Genest, L. Vinet // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 34 назв. — англ. |
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irk-123456789-1464062019-02-10T01:24:43Z The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) Vincent X. Genest Vinet, L. The 9j symbols of su(1,1) are studied within the framework of the generic superintegrable system on the 3-sphere. The canonical bases corresponding to the binary coupling schemes of four su(1,1) representations are constructed explicitly in terms of Jacobi polynomials and are seen to correspond to the separation of variables in different cylindrical coordinate systems. A triple integral expression for the 9j coefficients exhibiting their symmetries is derived. A double integral formula is obtained by extending the model to the complex three-sphere and taking the complex radius to zero. The explicit expression for the vacuum coefficients is given. Raising and lowering operators are constructed and are used to recover the relations between contiguous coefficients. It is seen that the 9j symbols can be expressed as the product of the vacuum coefficients and a rational function. The recurrence relations and the difference equations satisfied by the 9j coefficients are derived. 2014 Article The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) / Vincent X. Genest, L. Vinet // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 34 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C50; 81R05 DOI:10.3842/SIGMA.2014.108 http://dspace.nbuv.gov.ua/handle/123456789/146406 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 9j symbols of su(1,1) are studied within the framework of the generic superintegrable system on the 3-sphere. The canonical bases corresponding to the binary coupling schemes of four su(1,1) representations are constructed explicitly in terms of Jacobi polynomials and are seen to correspond to the separation of variables in different cylindrical coordinate systems. A triple integral expression for the 9j coefficients exhibiting their symmetries is derived. A double integral formula is obtained by extending the model to the complex three-sphere and taking the complex radius to zero. The explicit expression for the vacuum coefficients is given. Raising and lowering operators are constructed and are used to recover the relations between contiguous coefficients. It is seen that the 9j symbols can be expressed as the product of the vacuum coefficients and a rational function. The recurrence relations and the difference equations satisfied by the 9j coefficients are derived. |
| format |
Article |
| author |
Vincent X. Genest Vinet, L. |
| spellingShingle |
Vincent X. Genest Vinet, L. The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Vincent X. Genest Vinet, L. |
| author_sort |
Vincent X. Genest |
| title |
The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) |
| title_short |
The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) |
| title_full |
The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) |
| title_fullStr |
The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) |
| title_full_unstemmed |
The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1) |
| title_sort |
generic superintegrable system on the 3-sphere and the 9j symbols of su(1, 1) |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146406 |
| citation_txt |
The Generic Superintegrable System on the 3-Sphere and the 9j Symbols of su(1, 1)
/ Vincent X. Genest, L. Vinet // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 34 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-10T23:55:30Z |
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