The Quantum Superalgebra osp[subscript q] (1|2) and a q-Generalization of the Bannai-Ito Polynomials

The Quantum Superalgebra osp[subscript q] (1|2) and a q-Generalization of the Bannai-Ito Polynomials

The Racah problem for the quantum superalgebra osp[subscript 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 osp[subscript q] (1|2) are calculated explicitly in terms of basic orthogonal polynomials...

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Bibliographic Details
Main Authors: Vinet, Luc (Author), Zhedanov, Alexei (Author), Genest, Vincent (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: Springer Berlin Heidelberg, 2017-04-07T20:10:17Z.
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Summary:The Racah problem for the quantum superalgebra osp[subscript 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 osp[subscript 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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