
Journal of Lie Theory 17 (2007), No. 4, 791828 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 pacharon@mate.uncor.edu Juan Tirao CIEM  FaMAF, Universidad Nacional, Córdoba 5000, Argentina tirao@mate.uncor.edu The symmetric space duality between the complex hyperbolic plane H_{2}(C) = SU(2, 1) / U(2) and the complex projective plane P_{2}(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 H_{2}(C). Keywords: Dual Hermitian symmetric spaces, principal series, tensor product, multiplication formula, matrix hypergeometric function. MSC: 22E46, 33C45 [ Fulltextpdf (336 KB)] for subscribers only. 