Dual $-1$ Hahn polynomials: “Classical” polynomials beyond the Leonard duality

DOI10.1090/S0002-9939-2012-11469-8zbMath1300.33018arXiv1108.0132MaRDI QIDQ4907127

Luc Vinet, Satoshi Tsujimoto, Alexei Zhedanov

Publication date: 4 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.0132

zbMATH Keywords

classical orthogonal polynomialsdual \(q\)-Hahn polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items

The Dunkl-Coulomb problem in the plane ⋮ Symmetric abstract hypergeometric polynomials ⋮ Para-Bannai-Ito polynomials ⋮ Doubling (dual) Hahn polynomials: classification and applications ⋮ A Howe correspondence for the algebra of the \(\mathfrak{osp}(1 | 2)\) Clebsch-Gordan coefficients ⋮ Constructing bispectral dual Hahn polynomials ⋮ The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra ⋮ Bivariate Bannai-Ito polynomials ⋮ Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials ⋮ A unified construction of all the hypergeometric and basic hypergeometric families of orthogonal polynomial sequences ⋮ The non-symmetric Wilson polynomials are the Bannai–Ito polynomials ⋮ Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra ⋮ Superintegrability and the dual \(- 1\) Hahn algebra in superconformal quantum mechanics ⋮ Perfect state transfer in a spin chain without mirror symmetry

Cites Work

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• A Bochner theorem for Dunkl polynomials
• An exactly solvable spin chain related to Hahn polynomials
• Dunkl shift operators and Bannai-Ito polynomials
• A limit $q=-1$ for the big $q$-Jacobi polynomials
• Finite oscillator models: the Hahn oscillator
• A ‘missing’ family of classical orthogonal polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Orthogonal Polynomials, Duality and Association Schemes
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other

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