AUTOMORPHISM-INVARIANT REPRESENTATIONS OF REAL REDUCTIVE GROUPS

Abstract. We characterize representations of a connected real reductive group which are invariant under an automorphism of finite order. The intertwining operators constructed in this characterization are then used to prove a Paley-Wiener theorem for a class of real reductive groups twisted by involutions. 1. Introduction. Suppose G is a connected real reductive group (satisfying some customary hypotheses) and σ is an automorphism of finite order. There is an established characterization of the irreducible admissible representations of G in terms of (limits of) discrete series representations. The first goal of this work is to characterize similarly those admissible representations which are equivalent t