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Discrete group actions on Stein domains in complex Lie groups

Dehbia Achab·Frank Betten·Bernhard Kroetz
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Abstract

This paper deals with the analytic continuation of holomorphic automorphic forms on a Lie group $G$. We prove that for any discrete subgroup $Γ$ of $G$ there always exists a non-trivial holomorphic automorphic form, i.e., there exists a $Γ$-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 $Γ\bs S\subseteq Γ\bs G_\C$ separate the points.

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BibTeXRIS

Dehbia Achab, Frank Betten, Bernhard Kroetz. 2002-05-29. Discrete group actions on Stein domains in complex Lie groups. https://arxiv.org/abs/math/0004025

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