2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121221Let G be the group of F-points of a reductive group defined over F, $σ$ a rational involution of this group defined over F and H the group of fixed points of $σ$ . 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.Latex,42 pages. Augmented introduction, changes in section 2.7, added references, corrected typosRepresentation Theory22E50text