Generating function for the Bannai-Ito polynomials

DOI10.1090/proc/14158zbMath1477.33013arXiv1605.03407OpenAlexW2963080104MaRDI QIDQ4691327

Luc Vinet, Satoshi Tsujimoto, Geoffroy Bergeron

Publication date: 23 October 2018

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

Full work available at URL: https://arxiv.org/abs/1605.03407

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Cites Work

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• From \(\text{sl}_q(2)\) to a parabosonic Hopf algebra
• Dunkl shift operators and Bannai-Ito polynomials
• A Laplace-Dunkl equation on \(S^2\) and the Bannai-Ito algebra
• The generic superintegrable system on the 3-sphere and the \(9j\) symbols of \(\mathfrak{su}(1,1)\)
• Generating functions for the ${\mathfrak{osp}}(1| 2)$ Clebsch–Gordan coefficients
• A ‘missing’ family of classical orthogonal polynomials
• New construction of 3nj-symbols
• Coupling coefficients for Lie algebra representations and addition formulas for special functions
• Convolutions for Orthogonal Polynomials from Lie and Quantum Algebra Representations
• Realizations of su(1,1) and Uq(su(1,1)) and generating functions for orthogonal polynomials
• The Bannai–Ito algebra and a superintegrable system with reflections on the two-sphere
• The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra

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