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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.07766 |
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| _version_ | 1866915382021849088 |
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| author | Crampe, Nicolas Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei |
| author_facet | Crampe, Nicolas Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei |
| contents | The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as subalgebras Racah and Jacobi algebras of rank one. The dual realizations in terms of differential operators in the variable representation and in terms of difference operators in the degree representation are provided. Structure relations for the two variable Jacobi polynomials are obtained as a by product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The rank two Jacobi algebra Crampe, Nicolas Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei Mathematical Physics The quadratic rank two Jacobi algebra is identified from the relations obeyed by the bispectral operators of the two variable Jacobi polynomials orthogonal on the triangle. It is seen to admit as subalgebras Racah and Jacobi algebras of rank one. The dual realizations in terms of differential operators in the variable representation and in terms of difference operators in the degree representation are provided. Structure relations for the two variable Jacobi polynomials are obtained as a by product. |
| title | The rank two Jacobi algebra |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2507.07766 |