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The quantum superalgebra $\mathfrak{osp}_{q}(1|2)$ and a $q$-generalization of the Bannai-Ito polynomials
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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.
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Higher Rank Relations for the Askey-Wilson and $q$-Bannai-Ito Algebra
New commutation and q-commutation relations are proven for generators of the higher rank Askey-Wilson and q-Bannai-Ito algebras, extending the rank-one defining relations.
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