2010/02/28 by Heiko Gimperlein, Bernhard Krötz, Bernhard Kroetz +1
Mathematics · #Action (physics) #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Analytic function #Combinatorics #Global analytic function #Lie algebra #Lie group #Mathematics #Pure mathematics #Representation theory #Space (punctuation) #Topological group #Topology (electrical circuits) #math.RT #msc:22E45
paper · pdf · doi:10.1112/s0010437x11005392
published as Compositio Math. 147 (2011) 1581-1607 · Main file unchanged. Erratum added at the end
openalex publication_date 2011/06/01 · arxiv created 2016/03/11 · arxiv updated 2019/02/20 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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 .