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Journal of Lie Theory 17 (2007), No. 4, 791--828
Copyright Heldermann Verlag 2007

Three Term Recursion Relation for Spherical Functions Associated to the Complex Hyperbolic Plane

Inés Pacharoni
CIEM - FaMAF, Universidad Nacional, Córdoba 5000, Argentina

Juan Tirao
CIEM - FaMAF, Universidad Nacional, Córdoba 5000, Argentina

The symmetric space duality between the complex hyperbolic plane H2(C) = SU(2, 1) / U(2) and the complex projective plane P2(C) = SU(3) / U(2) also becomes apparent in the theory of matrix valued spherical functions associated to both spaces. This is stressed in this paper by proving a three term recursion relation for a family of matrix valued functions built up from the spherical functions associated to H2(C).

Keywords: Dual Hermitian symmetric spaces, principal series, tensor product, multiplication formula, matrix hypergeometric function.

MSC: 22E46, 33C45

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