Kinvi Kangni (Universite Felix Houphouet-Boigny)

Title: Spherical Grassmannian on a reductive Lie group
Abstract: Let $G$ be a locally compact group, $K$ a compact subgroup of $G$ and $% \delta $ an arbitrary class of irreducible unitary representations of $K$. The $p$-$\delta $-spherical Grassmannian $\mathcal{G}_{p,\delta }$ is an equivalence class of spherical functions of type $\delta $-positive of height $p$. In this talk, we construct some elements of $\mathcal{G}_{p,\delta }$ on reductive Lie group using a generalized Abel transform. And if the discret serie is not empty,we give a extension of Paley Wiener theorem using a compact Cartan subgroup of $G.$