Some Results on the Schwartz Space of $\Gamma\backslash G$

Abstract

Let $G$ be a connected semisimple Lie group with finite center. Let $\Gamma \subset G$ be a discrete subgroup. We study closed admissible irreducible subrepresentations of the space of distributions $\mathcal S(\Gamma \backslash G)'$ defined by Casselman, and their relations to automorphic forms.