The quantum superalgebra ${\mathfrak{osp}}_q(1|2)$ and a $q$-generalization of the Bannai-Ito polynomials

Abstract

The Racah problem for the quantum superalgebra ${\mathfrak{osp}}_q(1|2)$ is considered. The intermediate Casimir operators are shown to realize a $q$-deformation of the Bannai-Ito algebra. The Racah coefficients of ${\mathfrak{osp}}_q(1|2)$ are calculated explicitly in terms of basic orthogonal polynomials that $q$-generalize the Bannai-Ito polynomials. The relation between these $q$-deformed Bannai-Ito polynomials and the $q$-Racah/Askey-Wilson polynomials is discussed.

15 pages

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• The Bannai-Ito algebra and some applications
• A Dirac-Dunkl equation on $S^2$ and the Bannai-Ito algebra
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Cited by in corpus (5)

• The higher rank $q$-deformed Bannai-Ito and Askey-Wilson algebra
• Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra
• Centralizers of the superalgebra osp(1|2): the Brauer algebra as a quotient of the Bannai-Ito algebra
• The $q$-Bannai-Ito algebra and multivariate $(-q)$-Racah and Bannai-Ito polynomials
• Coupling coefficients of $s{u}_q(1,1)$ and multivariate $q$-Racah polynomials