Let G be a locally compact group, K a compact subgroup of G and \delta an arbitrary class of irreducible unitary representations of K.

If U is a topological completely irreducible representation of G on a Banach space E such that \delta is contained in the restriction of U to K, then there exists a spherical function \phi ^U of type \delta which is not trivial.

The height of \phi is the multiplicity p of \delta in the restriction to K of the representation U_{\phi } associated to \phi.

The p-\delta-spherical Grassmannian G_{p,\delta } is an equivalence class of spherical functions of type \delta-positive of height p.

In this talk, we'll construct some elements of G_{p,\delta } on a locally compact group, on a connected Lie group and on a reductive Lie group using a generalized Abel transform.

And, if the discret series of G is not empty, we'll give a extension of Paley Wiener theorem using a compact Cartan subgroup of G.

L'exposé sera à 10h utc (11h Paris) via zoom :

https://univ-nantes-fr.zoom.us/j/93782512911?pwd=ek5kUVNad3dIMHd6OWp0ZTZmQzZjUT09

ID de réunion : 937 8251 2911
Code secret : 540877