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

I. Pacharoni; J. Tirao

doi:10.5802/jolt.473

I. Pacharoni; J. Tirao

Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 791-828

Abstract

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).

Zbl

DOI: 10.5802/jolt.473

Classification: 22E46, 33C45
Keywords: Dual Hermitian symmetric spaces, principal series, tensor product, multiplication formula, matrix hypergeometric function

@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},
     doi = {10.5802/jolt.473},
     zbl = {1140.22011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.473/}
}

TY  - JOUR
AU  - I. Pacharoni
AU  - J. Tirao
TI  - Three Term Recursion Relation for Spherical Functions Associated to the Complex Hyperbolic Plane
JO  - Journal of Lie Theory
PY  - 2007
SP  - 791
EP  - 828
VL  - 17
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.473/
DO  - 10.5802/jolt.473
ID  - JOLT_2007_17_4_a4
ER  -

%0 Journal Article
%A I. Pacharoni
%A J. Tirao
%T Three Term Recursion Relation for Spherical Functions Associated to the Complex Hyperbolic Plane
%J Journal of Lie Theory
%D 2007
%P 791-828
%V 17
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.473/
%R 10.5802/jolt.473
%F JOLT_2007_17_4_a4

I. Pacharoni; J. Tirao. Three Term Recursion Relation for Spherical Functions Associated to the Complex Hyperbolic Plane. Journal of Lie Theory, Volume 17 (2007) no. 4, pp. 791-828. doi: 10.5802/jolt.473

Cited by Sources: