Geodesic
Three Term Recursion Relation for Spherical Functions Associated to the Complex Hyperbolic Plane
Journal of Lie Theory, Tome 17 (2007) no. 4, pp. 791-828

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Zbl

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).
Classification : 22E46, 33C45
Mots-clés : Dual Hermitian symmetric spaces, principal series, tensor product, multiplication formula, matrix hypergeometric function 
I. Pacharoni; J. Tirao. Three Term Recursion Relation for Spherical Functions Associated to the Complex Hyperbolic Plane. Journal of Lie Theory, Tome 17 (2007) no. 4, pp. 791-828. http://geodesic.mathdoc.fr/item/JOLT_2007_17_4_a4/
@article{JOLT_2007_17_4_a4,
     author = {I. Pacharoni and J. Tirao},
     title = {Three {Term} {Recursion} {Relation} for {Spherical} {Functions} {Associated} to the {Complex} {Hyperbolic} {Plane}},
     journal = {Journal of Lie Theory},
     pages = {791--828},
     year = {2007},
     volume = {17},
     number = {4},
     zbl = {1140.22011},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_4_a4/}
}
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