Spherical Functions for the Semisimple Symmetric Pair (Sp(2, R), SL(2, C))

Moriyama, Tomonori

Canadian journal of mathematics, Tome 54 (2002) no. 4, pp. 828-865

Résumé

Let $\pi $ be an irreducible generalized principal series representation of $G\,=\,\text{Sp}\left( 2,\,\mathbb{R} \right)$ induced from its Jacobi parabolic subgroup. We show that the space of algebraic intertwining operators from $\pi $ to the representation induced from an irreducible admissible representation of $\text{SL}\left( 2,\,\mathbb{C} \right)$ in $G$ is at most one dimensional. Spherical functions in the title are the images of $K$ -finite vectors by this intertwining operator. We obtain an integral expression of Mellin-Barnes type for the radial part of our spherical function.

Détail

DOI : 10.4153/CJM-2002-032-2

Mots-clés : 22E45, 11F70

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