Matrix orthogonal polynomials and group representations

I. PACHARONI

Cambridge

Congreso; Discrete Systems and Special Functions (DISW04); 2009

Newton Institute for Mathematical Science

In the scalar case, it is well known that classical orthogonal polynomials can be obtained as the zonal spherical functions of compact Riemannian symmetric space of rank one. The main purpose of this talk is to exhibit the interplay among the matrix orthogonal polynomials, the matrix hypergeometric functions and the matrix spherical functions in the context of the complex projective space. Also an example in two variables, related with the grassmannian manifolds will be considered.