Discrete group actions on Stein domains in complex Lie groups
Abstract
This paper deals with the analytic continuation of holomorphic automorphic forms on a Lie group $G$. We prove that for any discrete subgroup $\Gamma$ of $G$ there always exists a nontrivial holomorphic automorphic form, i.e., there exists a $\Gamma$spherical unitary highest weight representation of $G$. Holomorphic automorphic forms have the property that they analytically extend to holomorphic functions on a complex Ol'shanski\uı semigroup $S\subeq G_\C$. As an application we prove that the bounded holomorphic functions on $\Gamma\bs S\subseteq \Gamma\bs G_\C$ separate the points.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2000
 arXiv:
 arXiv:math/0004025
 Bibcode:
 2000math......4025A
 Keywords:

 Representation Theory
 EPrint:
 26 pages, to appear in Forum Math