%0 Journal Article
%T Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules
%A Heiko Gimperlein
%A Bernhard Kroetz
%A Henrik Schlichtkrull
%J Mathematics
%D 2010
%I arXiv
%R 10.1112/S0010437X11005392
%X In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra A(G) of analytic functions of rapid decay. For reductive groups every Harish-Chandra module V is shown to admit a unique tempered analytic globalization, which is generated by V and A(G) and which embeds as the space of analytic vectors in all Banach globalizations of V.
%U http://arxiv.org/abs/1002.4345v1