The spherical functions and the Central limit theorem on SU(2,2)/ S( U(2)× U(2))

Abstract

Let G = SU(2,2), K = S( U(2) × U(2)), and for l ∈ Z , let { τ l } l ∈ z be a one-dimensional K-type and let E l be the line bundle over G/K associated to τ 1. It is shown that the τ l-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.