Discrete group actions on Stein domains in complex Lie groups

2000/04/30 by Dehbia Achab, Frank Betten, Bernhard Kroetz
Mathematics · #math.RT

paper · pdf

published as Forum Math. 16 (1) (2004), 37--68 · 26 pages, to appear in Forum Math

arxiv created 2002/05/29 · arxiv updated 2009/11/30

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⊆ Γ\bs G_\C separate the points.

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