Residue representations - The rank one case

With each resonance of the Laplacian acting on compactly supported sections a homogeneous vector bundle over Riemannian symmetric space non-compact type, One can associate residue representation. The purpose this paper is to study them. assumed have rank-one but irreducible representation {\tau} K defining arbitrary. We give an algorithm that aims at determining if these representations are irreducible, finding their Langlands parameters, Gelfand-Kirillov dimensions and wave front sets. As example, we apply p-forms in cases all classical real Lie groups.