Some results on harmonic analysis on reductive p-adic symmetric spaces

by Patrick Delorme, Institut de Mathématiques de Luminy, Université de la Méditerranée.

I will describe first basic facts on p-adic symmetric spaces, in particular results of A.Helminck with S.P. Wang and G. Helminck.
I will describe the Cartan decomposition for p-adic symmetric spaces (Benoist-Oh, Delorme-Sécherre).
I will describe results of Lagier, Kato-Takano and I on $H$-fixed linear forms on smooth-modules and Jacquet modules. This leads to the definition of the constant term of smooth functions on a p-adic symmetric space and of cuspidal functions. Actually all of this works also for mixed models, which include Whittaker models and reductive symmetric spaces. Finiteness theorems will be described.
The rational continuation of Eisenstein integrals will be described (Blanc-Delorme).