Meta Algebras and Special Functions: the Racah Case
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908923422834688 |
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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 | Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its finite-dimensional representations. These functions are identified as overlap coefficients between eigensolutions of generalized and standard eigenvalue problems posited on the representation space. The approach naturally yields their orthogonality relations and bispectral properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28839 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Meta Algebras and Special Functions: the Racah Case Crampé, Nicolas Labriet, Quentin Morey, Lucia Tsujimoto, Satoshi Vinet, Luc Zhedanov, Alexei Classical Analysis and ODEs Mathematical Physics Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its finite-dimensional representations. These functions are identified as overlap coefficients between eigensolutions of generalized and standard eigenvalue problems posited on the representation space. The approach naturally yields their orthogonality relations and bispectral properties. |
| title | Meta Algebras and Special Functions: the Racah Case |
| topic | Classical Analysis and ODEs Mathematical Physics |
| url | https://arxiv.org/abs/2603.28839 |