We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Analytic representation theory of Lie groups: general theory and analytic globalizations of Harish-Chandra modules.
- Authors
Gimperlein, Heiko; Krötz, Bernhard; Schlichtkrull, Henrik
- 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 (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 (G) and which embeds as the space of analytic vectors in all Banach globalizations of V.
- Subjects
LIE groups; REPRESENTATIONS of algebras; MODULES (Algebra); ANALYTIC functions; VECTOR spaces; TOPOLOGICAL groups; MATHEMATICAL analysis
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1581
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X11005392