Superelliptic Affine Lie algebras and orthogonal polynomials
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913953434566656 |
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| author | Santos, Felipe Albino dos Neklyudov, Mikhail Futorny, Vyacheslav |
| author_facet | Santos, Felipe Albino dos Neklyudov, Mikhail Futorny, Vyacheslav |
| contents | We construct two families of orthogonal polynomials associated with the universal central extensions of the superelliptic Lie algebras. These polynomials satisfy certain fourth order linear differential equations, and one of the families is a particular collection of associated ultraspherical polynomials. We show that the generating functions of the polynomials satisfy fourth order linear PDEs. Since these generating function can be represented by superelliptic integrals, we have examples of linear PDEs of fourth order with explicit solutions without complete integrability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Superelliptic Affine Lie algebras and orthogonal polynomials Santos, Felipe Albino dos Neklyudov, Mikhail Futorny, Vyacheslav Representation Theory Mathematical Physics Classical Analysis and ODEs 34C47 (primary) 17B65, 22E65 (secondary) We construct two families of orthogonal polynomials associated with the universal central extensions of the superelliptic Lie algebras. These polynomials satisfy certain fourth order linear differential equations, and one of the families is a particular collection of associated ultraspherical polynomials. We show that the generating functions of the polynomials satisfy fourth order linear PDEs. Since these generating function can be represented by superelliptic integrals, we have examples of linear PDEs of fourth order with explicit solutions without complete integrability. |
| title | Superelliptic Affine Lie algebras and orthogonal polynomials |
| topic | Representation Theory Mathematical Physics Classical Analysis and ODEs 34C47 (primary) 17B65, 22E65 (secondary) |
| url | https://arxiv.org/abs/2402.02947 |