Matrix valued orthogonal polynomials of the Jacobi type: the role of group representation theory

F. A. GRUNBAUM, I. PACHARONI, J.TIRAO

ANNALES DE L INSTITUT FOURIER

Instituto Fourier.

Lugar: Paris; Año: 2005 vol. 55 p. 2051 - 2068

0373-0956

The main purpose of this paper is to present new families of Jacobi type matrix valued orthogonal polynomials obtained from the underlying group SU(n) and its representations. These polynomials are eigenfunctions of some symmetric second order hypergeometric differential operator with matrix coefficients. The final result holds for arbitrary values of the parameters $alpha,eta >-1$, but it is derived only for those values that come from the group theoretical setup.