Little and big q-Jacobi polynomials and the Askey–Wilson algebra

  • Pascal Baseilhac
  • Xavier Martin
  • Luc VinetEmail author
  • Alexei Zhedanov


The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey–Wilson algebra. The operators that these polynomials respectively diagonalize are identified within the Askey–Wilson algebra generated by twisted primitive elements of \(\mathfrak U_q(sl(2))\). The little q-Jacobi operator and a tridiagonalization of it are shown to realize the equitable embedding of the Askey–Wilson algebra into \(\mathfrak U_q(sl(2))\).


Askey–Wilson algebra Tridiagonalization Orthogonal polynomials 

Mathematics Subject Classification

81R50 81R10 81U15 39A70 33D50 39A13 



We thank Paul Terwilliger for comments. L.V. would like to express his gratitude for the hospitality extended to him by the Institut Denis-Poisson of the Université François-Rabelais de Tours as Chercheur Invité where most of this research was carried out.


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Authors and Affiliations

  1. 1.Institut Denis-Poisson CNRS/UMR 7013 - Université de Tours - Université d’OrléansToursFrance
  2. 2.Centre de Recherches MathématiquesUniversité de MontréalMontrealCanada
  3. 3.Department of Mathematics, Information SchoolRenmin University of ChinaBeijingChina

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