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

Abstract

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.

Main file unchanged. Erratum added at the end

References in corpus (3)

• Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules
• Smooth Frechet Globalizations of Harish-Chandra Modules
• Continuity of LF-algebra representations associated to representations of Lie groups

Cited by in corpus (5)

• Analytic representation theory of Lie groups: General theory and analytic globalizations of Harish--Chandra modules
• Volume growth, temperedness and integrability of matrix coefficients on a real spherical space
• Continuity of LF-algebra representations associated to representations of Lie groups
• Analytic Dirac approximation for real linear algebraic groups
• Strong factorization of ultradifferentiable vectors associated with compact Lie group representations