Superspace realizations of the Bannai-Ito algebra

DOI10.1007/s11005-023-01731-6arXiv2306.02714OpenAlexW4387612982MaRDI QIDQ6084684

Hendrik De Bie, Luc Vinet, Plamen Iliev, Nicolas Crampé

Publication date: 6 November 2023

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.02714

zbMATH Keywords

Jacobi polynomialssuperspacesuper Lie algebra

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05) Differential algebra (12H05) Special polynomials in general fields (12E10) Classical hypergeometric functions, ({}_2F_1) (33C05) Exterior algebra, Grassmann algebras (15A75)

Cites Work

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• The \(\mathbb{Z}_2^n\) Dirac-Dunkl operator and a higher rank Bannai-Ito algebra
• Superintegrability in two dimensions and the Racah-Wilson algebra
• Dunkl shift operators and Bannai-Ito polynomials
• An embedding of the Bannai-Ito algebra in \(\mathcal U(\mathfrak{osp}(1,2))\) and \(-1\) polynomials
• Algebraic combinatorics. Translated from the Japanese
• Embeddings of the Racah algebra into the Bannai-Itô algebra
• The classification of Leonard triples of Racah type
• Lie theory and special functions
• The non-symmetric Wilson polynomials are the Bannai–Ito polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• A higher rank Racah algebra and the $\mathbb{Z}_2^n$ Laplace–Dunkl operator
• Bargmann and Barut-Girardello models for the Racah algebra
• The Bannai-Ito polynomials as Racah coefficients of the $sl_{-1}(2)$ algebra
• The equitable Racah algebra from three $\mathfrak {su}(1,1)$ algebras

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