Superelliptic Affine Lie algebras and orthogonal polynomials
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 polyno...
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Cambridge University Press
2025-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100741/type/journal_article |
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| author | Felipe Albino dos Santos Mikhail Neklyudov Vyacheslav Futorny |
| author_facet | Felipe Albino dos Santos Mikhail Neklyudov Vyacheslav Futorny |
| author_sort | Felipe Albino dos Santos |
| collection | DOAJ |
| description | 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 functions can be represented by superelliptic integrals, we have examples of linear PDEs of fourth order with explicit solutions without complete integrability. |
| format | Article |
| id | doaj-art-cdb6f6f71bbd4bab9b20dde7cc0179cc |
| institution | DOAJ |
| issn | 2050-5094 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-cdb6f6f71bbd4bab9b20dde7cc0179cc2025-08-20T03:12:46ZengCambridge University PressForum of Mathematics, Sigma2050-50942025-01-011310.1017/fms.2025.10074Superelliptic Affine Lie algebras and orthogonal polynomialsFelipe Albino dos Santos0https://orcid.org/0000-0002-3133-4877Mikhail Neklyudov1https://orcid.org/0000-0002-8238-5017Vyacheslav Futorny2https://orcid.org/0000-0002-4701-8879https://ror.org/006nc8n95 Faculdade de Computação e Informática, Universidade Presbiteriana Mackenzie, Rua da Consolação, 930, SP 01302-907 São Paulo, Brazil; E-mail:Departamento de Matematica, https://ror.org/02263ky35 Universidade Federal do Amazonas, 1200, Av. General Rodrigo Octavio, Manaus, AM 69067-005, BrazilShenzhen International Center for Mathematics, https://ror.org/049tv2d57 Southern University of Science and Technology, 1088 Xueyuan Avenue, Shenzhen, 518055, P.R. China; E-mail: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 functions can be represented by superelliptic integrals, we have examples of linear PDEs of fourth order with explicit solutions without complete integrability.https://www.cambridge.org/core/product/identifier/S2050509425100741/type/journal_article17B0517B6542C05 |
| spellingShingle | Felipe Albino dos Santos Mikhail Neklyudov Vyacheslav Futorny Superelliptic Affine Lie algebras and orthogonal polynomials Forum of Mathematics, Sigma 17B05 17B65 42C05 |
| title | Superelliptic Affine Lie algebras and orthogonal polynomials |
| title_full | Superelliptic Affine Lie algebras and orthogonal polynomials |
| title_fullStr | Superelliptic Affine Lie algebras and orthogonal polynomials |
| title_full_unstemmed | Superelliptic Affine Lie algebras and orthogonal polynomials |
| title_short | Superelliptic Affine Lie algebras and orthogonal polynomials |
| title_sort | superelliptic affine lie algebras and orthogonal polynomials |
| topic | 17B05 17B65 42C05 |
| url | https://www.cambridge.org/core/product/identifier/S2050509425100741/type/journal_article |
| work_keys_str_mv | AT felipealbinodossantos superellipticaffineliealgebrasandorthogonalpolynomials AT mikhailneklyudov superellipticaffineliealgebrasandorthogonalpolynomials AT vyacheslavfutorny superellipticaffineliealgebrasandorthogonalpolynomials |