A sequence of matrix valued orthogonal polynomials associated to spherical functions

2007/02/16 by Inés Pacharoni, Pacharoni, I., Pablo Román +1 · 1 citation
Computer Science · Mathematics · #33C45 #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0702494

openalex publication_date 2007/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials P_nn, with respect to a weight W, that are eigenfunctions of a second order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We also find other second order differential operator E symmetric with respect to W and we describe the algebra generated by D and E.

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• Matrix-valued bispectral discrete orthogonal polynomials

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