Some results on the Schwartz space of Γ \ G

Sa？etak Let G be a connected semisimple Lie group with finite center. Let Γ ？ G be a discrete subgroup. We study closed admissible irreducible subrepresentations of the space of distributions S(Γ \ G)' defined by Casselman, and their relations to automorphic forms on Γ \ G when Γ is a congruence subgroup