Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules

Details Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules

2010-02-23

arxiv.org/abs/1002.4345v1

Mathematics

Representation Theory

Scientific paper

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.

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