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Transformation Groups

, Volume 24, Issue 2, pp 467–510 | Cite as

CLASSIFICATION OF REDUCTIVE REAL SPHERICAL PAIRS II. THE SEMISIMPLE CASE

  • F. KNOP
  • B. KRÖTZ
  • T. PECHER
  • H. SCHLICHTKRULLEmail author
Article
  • 45 Downloads

Abstract

If \( \mathfrak{g} \) is a real reductive Lie algebra and \( \mathfrak{h}\subset \mathfrak{g} \) is a subalgebra, then the pair (\( \mathfrak{h},\mathfrak{g} \)) is called real spherical provided that \( \mathfrak{g}=\mathfrak{h}+\mathfrak{p} \) for some choice of a minimal parabolic subalgebra \( \mathfrak{p}\subset \mathfrak{g} \). This paper concludes the classification of real spherical pairs (\( \mathfrak{h},\mathfrak{g} \)), where \( \mathfrak{h} \) is a reductive real algebraic subalgebra. More precisely, we classify all such pairs which are strictly indecomposable, and we discuss (in Section 6) how to construct from these all real spherical pairs. A preceding paper treated the case where \( \mathfrak{g} \) is simple. The present work builds on that case and on the classification by Brion and Mikityuk for the complex spherical case.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • F. KNOP
    • 1
  • B. KRÖTZ
    • 2
  • T. PECHER
    • 2
  • H. SCHLICHTKRULL
    • 3
    Email author
  1. 1.Department MathematikFAU Erlangen-NürnbergErlangenGermany
  2. 2.Institut für MathematikUniversität PaderbornPaderbornGermany
  3. 3.Department of MathematicsUniversity of CopenhagenCopenhagen ∅Denmark

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