The non-symmetric Wilson polynomials are the Bannai–Ito polynomials

DOI10.1090/proc/13141zbMath1354.33010arXiv1507.02995OpenAlexW2962715448MaRDI QIDQ2827371

Alexei Zhedanov, Luc Vinet, Vincent X. Genest

Publication date: 19 October 2016

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

Full work available at URL: https://arxiv.org/abs/1507.02995

zbMATH Keywords

double affine Hecke algebrasBannai-Ito polynomialsBannai-Ito algebrasnon-symmetric Wilson polynomials

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Connections of hypergeometric functions with groups and algebras, and related topics (33C80)

Related Items (17)

The dual pair \(Pin(2n) \times \mathfrak{osp}(1|2)\), the Dirac equation and the Bannai-Ito algebra ⋮ The space of Dunkl monogenics associated with \(\mathbb{Z}_2^3\) ⋮ The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra ⋮ An embedding of the Bannai-Ito algebra in \(\mathcal U(\mathfrak{osp}(1,2))\) and \(-1\) polynomials ⋮ Little and big \(q\)-Jacobi polynomials and the Askey-Wilson algebra ⋮ Superspace realizations of the Bannai-Ito algebra ⋮ Finite-dimensional irreducible modules of the Bannai-Ito algebra at characteristic zero ⋮ Racah problems for the oscillator algebra, the Lie algebra \(\mathfrak{sl}_n\), and multivariate Krawtchouk polynomials ⋮ The Racah algebra as a subalgebra of the Bannai-Ito algebra ⋮ Dualities in the q‐Askey Scheme and Degenerate DAHA ⋮ Bannai–Ito algebras and the osp(1;2) superalgebra ⋮ Bivariate Bannai-Ito polynomials ⋮ Finite-dimensional modules of the universal Racah algebra and the universal additive DAHA of type \((C_1^\vee,C_1)\) ⋮ Finite-dimensional modules of the universal Askey-Wilson algebra and DAHA of type \((C_1^\vee ,C_1)\) ⋮ The higher rank \(q\)-deformed Bannai-Ito and Askey-Wilson algebra ⋮ 𝔬𝔰𝔭(1,2) and generalized Bannai–Ito algebras ⋮ Double affine Hecke algebra of rank 1 and orthogonal polynomials on the unit circle

Cites Work

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• Bispectrality of the complementary Bannai-Itō polynomials
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• Fourier transforms related to a root system of rank 1
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• Commuting difference operators with polynomial eigenfunctions
• Dual $-1$ Hahn polynomials: “Classical” polynomials beyond the Leonard duality
• The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra

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