The dynamical algebra of the generic superintegrable model on the two-sphere
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910176043335680 |
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| author | Crampé, Nicolas Labriet, Quentin Morey, Lucia Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei |
| author_facet | Crampé, Nicolas Labriet, Quentin Morey, Lucia Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei |
| contents | The rank two Jacobi algebra $\mathfrak{J}_2$ is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of this algebra is obtained from its embedding in $\mathfrak{su}(1,1)^{\otimes 3}$. The exact solution of the model is derived algebraically from this representation. The wavefunctions are found to be expressed in terms of two-variable Jacobi polynomials whose characterization is a by-product of the algebraic treatment of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26122 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The dynamical algebra of the generic superintegrable model on the two-sphere Crampé, Nicolas Labriet, Quentin Morey, Lucia Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei Mathematical Physics Representation Theory The rank two Jacobi algebra $\mathfrak{J}_2$ is identified as the dynamical algebra of the generic quadratic superintegrable model on the two-sphere. The physical representation of this algebra is obtained from its embedding in $\mathfrak{su}(1,1)^{\otimes 3}$. The exact solution of the model is derived algebraically from this representation. The wavefunctions are found to be expressed in terms of two-variable Jacobi polynomials whose characterization is a by-product of the algebraic treatment of the model. |
| title | The dynamical algebra of the generic superintegrable model on the two-sphere |
| topic | Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2604.26122 |