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_l. 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.

Key words: Spherical function, central limit theorem, hypergeometric function