A Note on $\mathfrak{su}(2)$ Models and the Biorthogonality of Generating Functions of Krawtchouk Polynomials

C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (2) 2021, pp. 46-62
(Received: 2021-04-03 )

Luc Vinet, FRSC ,Centre de Recherches Mathematiques, Universite de Montreal, P.O. Box 6128, Centre-ville Station, Montreal (Quebec), H3C 3J7, Canada and Centre de Recherches Mathematiques, Universite de Montreal, P.O. Box 6128, Centre-ville Station, Montreal (Quebec), H3C 3J7, Canada; e-mail: vinet@CRM.UMontreal.CA

Alexei Zhendanov, School of Mathematics, Renmin University of China, Beijing, 100872, China; e-mail: zhedanov@yahoo.com

Abstract/Résumé:

Eigenvalue problems on irreducible \(\mathfrak{su}(2)\) modules and their adjoints are considered in the Bargmann, Barut-Girardello and finite difference models. The biorthogonality relations that arise between the corresponding generating functions of the Krawtchouk polynomials are sorted out. A link with Padé approximation is made.

Des problèmes aux valeurs propres sur les modulesirréductibles de \(\mathfrak{su}(2)\) et leurs adjoints sont examinés dans les modèles de Bargmann, Barut–Girardello et aux différences finies. Les relations de biorthogonalité qui apparaissent entre les fonctions génératrices correspondantes des polynômes de Krawtchouk sont identifiées. Un lien avec l’approximation de Padé est fait.

Keywords: Krawtchouk polynomials, Pade approximation., biorthogonality, generating functions, su(2) models

AMS Subject Classification: Representations; algebraic theory (weights), Orthogonal polynomials and functions of hypergeometric type (Jacobi; Laguerre; Hermite; Askey scheme; etc.), Pad_¸ approximation 17B10, 33C45, 41A21

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