Domains Of Holomorphy For Irreducible Admissible Uniformly Bounded Banach Representations Of Simple Lie Groups View Full Text


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Article Info

DATE

2018-09

AUTHORS

G. LIU, A. PARTHASARATHY

ABSTRACT

In this note, we address a question raised by B. Krötz on the classification of G-invariant domains of holomorphy for irreducible admissible Banach representations of connected non-compact simple real linear Lie groups G. When G is not of Hermitian type, we give a complete description of such G-invariant domains for irreducible admissible uniformly bounded representations on reflexive Banach spaces and, in particular, for all irreducible uniformly bounded Hilbert representations. When the group G is Hermitian, we determine such G-invariant domains only when the representations considered are highest or lowest weight representations. More... »

PAGES

755-764

References to SciGraph publications

  • 2008-12. Analysis on the Crown Domain in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 2007-03. Property (T) and rigidity for actions on Banach spaces in ACTA MATHEMATICA
  • 2005-02. Holomorphic extensions of representations: (ii) geometry and harmonic analysis in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 2008-05. Domains of holomorphy for irreducible unitary representations of simple Lie groups in INVENTIONES MATHEMATICAE
  • 2008. Applications of Representation Theory to Harmonic Analysis of Lie Groups (and Vice Versa) in REPRESENTATION THEORY AND COMPLEX ANALYSIS
  • 1990-03. On Stein extensions of real symmetric spaces in MATHEMATISCHE ANNALEN
  • 2014-01. Smooth Fréchet globalizations of Harish-Chandra modules in ISRAEL JOURNAL OF MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1007/s00031-017-9468-z

    DOI

    http://dx.doi.org/10.1007/s00031-017-9468-z

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