Funciones esféricas y el operador hipergeométrico matricial

P. ROMÁN Y J. TIRAO

Universidad Nacional del Sur, Bahía Blanca

Congreso; Reunión Anual de la Unión Mattemática Argentina; 2006

Unión Mattemática Argentina

The main purpose of this paper is to compute all irreducible spherical functions F of any K-type associated to the dual symmetric pairs (G,K)=(SU(3),U(2)) and (SU(2,1),U(2)). This is accomplished by associating to F a vector valued function H=H(u) of a real variable u, analytic at u=0, which is a simultaneous eigenfunction of two second order differential operators with matrix coefficients.  One of them comes from the Casimir operator of G and we prove that it is conjugated to a hypergeometric operator, allowing us to express the function H in terms of a matrix valued hypergeometric function.