Matrix Valued Spherical Functions Associated to the Three Dimensional Hyperbolic Space
نویسنده
چکیده
The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2,C) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space H = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisting involving Hahn polynomials we uncouple one of the systems and express the entries of H in terms of Gauss’ functions 2F1. Just as in the compact instance treated in [GPT] there is a useful role for a special class of generalized hypergeometric functions p+1Fp.
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