The principal series for a reductive symmetric space. II. Eisenstein integrals

Abstract

In this paper we develop a theory of Eisenstein integrals related to the principal series for a reductive symmetric space G=H: Here G is a real reductive group of Harish-Chandra's class, ? an involution of G and H an open subgroup of the group G ? of xed points for ?: The group G itself is a symmetric space for the left right action of G G : we refer to this setting as the group case. Up to a normalization, our Eisenstein integrals generalize those of Harish-Chandra [18] associated with a minimal parabolic subgroup in the group case.