Superelliptic Affine Lie algebras and orthogonal polynomials
Abstract 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.
Authors
- Felipe Albino dos Santos (ORCID: https://orcid.org/0000-0002-3133-4877)
- Vyacheslav Futorny (ORCID: https://orcid.org/0000-0002-4701-8879)
- Mikhail Neklyudov (ORCID: https://orcid.org/0000-0002-8238-5017)
Institutions
- Universidade Presbiteriana Mackenzie (BR)
- Southern University of Science and Technology (CN)
- Universidade Federal do Amazonas (BR)
Publication Details
- Journal
- Forum of Mathematics Sigma
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1017/fms.2025.10074
- Primary Topic
- Nonlinear Waves and Solitons
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Universidade Federal do Amazonas
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Universidade Presbiteriana Mackenzie
- National Natural Science Foundation of China-Henan Joint Fund