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

Let G = SU(2,2), K = S(U(2) × U(2)), and for l ∈ Z, let {τl} l ∈ z be a one-dimensional K-type and let El be the line bundle over G/K associated to τ1. It is shown that the τl-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.