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F. Alberto Grünbaum; Inés Pacharoni; Juan Alfredo Tirao
Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory
(Polynômes orthogonaux matriciels du type de Jacobi : le rôle de la théorie de représentations des groupes)
Annales de l'institut Fourier, 55 no. 6 (2005), p. 2051-2068, doi: 10.5802/aif.2151
Article PDF | Analyses MR 2187945 | Zbl 1082.33006
Class. Math.: 33C45, 22E45
Mots clés: polynômes orthogonaux matriciels, polynômes de Jacobi

Résumé - Abstract

Le résultat principal du présent article est la construction d'une nouvelle famille de poly\-nômes orthogonaux matriciels, du type de Jacobi. Ces polynômes proviennent du groupe sous-jacent $SU(n)$ et de ses représentations : ce sont des fonctions propres d'un opérateur différentiel symé\-trique du second ordre, hypergéométrique et à valeurs matricielles. Le résultat final est valable pour des valeurs arbitraires des paramètres $\alpha,\beta >-1$, mais est dérivé uniquement pour les valeurs provenant de la théorie des groupes.

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