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

## TL;DR

This paper investigates the structure of the Schwartz space of a quotient of a semisimple Lie group by a discrete subgroup, focusing on distribution subrepresentations and their connection to automorphic forms.

## Contribution

It provides new insights into the admissible irreducible subrepresentations of distribution spaces on quotient spaces of semisimple Lie groups, linking them to automorphic forms.

## Key findings

- Characterization of subrepresentations in the Schwartz space of mma G
- Relations established between distribution subrepresentations and automorphic forms
- Advances in understanding the representation theory of mma G quotients

## 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.