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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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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Vincent X. Genest

  2. Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, QC, H3C 3J7, Canada

    Luc Vinet

  3. Donetsk Institute for Physics and Technology, Donetsk, 83114, Ukraine

    Alexei Zhedanov

Authors
  1. Vincent X. Genest
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  2. Luc Vinet
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  3. Alexei Zhedanov
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Correspondence to Vincent X. Genest.

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Communicated by N. Reshetikhin

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Genest, V.X., Vinet, L. & Zhedanov, A. The Quantum Superalgebra \({\mathfrak{osp}_{q}(1|2)}\) and a q-Generalization of the Bannai–Ito Polynomials. Commun. Math. Phys. 344, 465–481 (2016). https://doi.org/10.1007/s00220-016-2647-2

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  • DOI: https://doi.org/10.1007/s00220-016-2647-2

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