Letters in Mathematical Physics

, Volume 108, Issue 7, pp 1623–1634 | Cite as

An embedding of the Bannai–Ito algebra in \(\mathscr {U}(\mathfrak {osp}(1,2))\) and \(-1\) polynomials

  • Pascal Baseilhac
  • Vincent X. Genest
  • Luc VinetEmail author
  • Alexei Zhedanov


An embedding of the Bannai–Ito algebra in the universal enveloping algebra of \(\mathfrak {osp}(1,2)\) is provided. A connection with the characterization of the little \(-1\) Jacobi polynomials is found in the holomorphic realization of \(\mathfrak {osp}(1,2)\). An integral expression for the Bannai–Ito polynomials is derived as a corollary.


Bannai–Ito algebra Quantum groups Orthogonal polynomials Integral representations 

Mathematics Subject Classification

81Q80 81R10 33C45 



PB, VXG and AZ acknowledge the hospitality of the CRM and LV that of the Université de Tours where parts of the reported research have been realized. PB is supported by C.N.R.S. VXG holds a postdoctoral fellowship from the Natural Science and Engineering Research Council (NSERC) of Canada. LV is grateful to NSERC for support through a discovery grant.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Physique Théorique CNRS/UMR 7350, Fédération Denis Poisson FR2964Université de ToursToursFrance
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Centre de Recherches MathématiquesUniversité de MontréalMontréalCanada
  4. 4.Department of Mathematics, School of InformationRenmin University of ChinaBeijingChina

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