Une fonction zêta associée à certaines familles d'espaces symétriques réels

Abstract

For certain families of real symmetric spaces ( G/H i ) i=1,…, where each G/H i can be realized as a connected component of the complementary set of an irreducible hypersurface, we construct a Zeta function which is associated to representations of the H i-spherical principal series of G, and we prove its functional equation. These families of symmetric spaces are the open orbits of the real prehomogeneous vector spaces of commutative parabolic type, or in an equivalent language, those coming from the real simple Jordan algebras.