Vecteurs distributions H-invariants de representations induites, pour un espace symetrique reductif p-adique G/H

Abstract

Let G be the group of F-points of a reductive group defined over F, $\sigma$ a rational involution of this group defined over F and H the group of fixed points of $\sigma$ . We built rational families of H-fixed vectors in the dual of generalized principal series, using smooth homology of groups. Results of A.G.Helminck,S.P.Wang and A.G.Helminck,G.F.Helminck on the structure of $\mathbb F$-varieties are also essential.