A sequence of matrix valued orthogonal polynomials associated to spherical functions

Details A sequence of matrix valued orthogonal polynomials associated to spherical functions A sequence of matrix valued orthogonal polynomials associated to spherical functions

2007-02-16

arxiv.org/abs/math/0702494v1

Mathematics

Representation Theory

Scientific paper

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {P_n}_n, 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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