Jan Felipe van Diejen, Universidad de Chile, Chile
e-mail: vandiej@uchile.cl

Determinantal Formulas for Zonal Spherical Functions
on Hyperboloids

(joint with A.N. Kirillov)

Abstract

We construct determinantal expressions for the zonal spherical functions on the hyperboloids $H^{p,q}=SO_0(p,q;\mathbb{R})/SO_0(p-1,q;\mathbb{R})$ with $p,q$ odd (and larger than $1$). This gives rise to explicit evaluation formulas forhypergeometric series representing half-integer parameter families of Jacobi functions and (via specialization) Jacobi polynomials.