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2 results

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

  • Part of
  • Heiko Gimperlein, Bernhard Krötz, Henrik Schlichtkrull
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 5 / September 2011
    Published online by Cambridge University Press:
    01 June 2011, pp. 1581-1607
    Print publication:
    September 2011
    • Article
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  • 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.