The Harish-Chandra Realization for Non-Symmetric Domains in ℂn

  • R. Penney
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 20)


Let D ⊂ ℂn be a bounded, homogeneous domain. This means that the group Aut (D) of bi-holomorphisms of D acts transitively on D. Let G be the component of the identity in Aut (D). It is known that G is a Lie group.


Jordan Algebra Isotropy Subgroup Euclidian Jordan Algebra Cone Versus Algebraic Subgroup 
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  1. [B]
    R Bernat et al.,Représentations des groupes de Lie résoluble, Dunod Paris, 1972Google Scholar
  2. [Do]
    S. Dorfmeister, Quasi-symmetric Siegel domains and the automorphisms of homogeneous Siegel domains,Amer. J. Math102 (1980), 537 – 563MathSciNetMATHCrossRefGoogle Scholar
  3. [HC]
    Harish-Chandra, Representations of semi-simple Lie groups, IV,Amer. J. Math.77 (1955), 743–777MathSciNetMATHCrossRefGoogle Scholar
  4. [Ku]
    S. Kaneyuki, Homogeneous Bounded Domains and Siegel Domains,Lecture Notes in Mathematics241 (1971), Springer-Verlag, BerlinGoogle Scholar
  5. [Kl]
    J. Koszul, Sur la forme hermitienne canonique des espaces homogenes complexes,Canad. J. Math.7 (1955), 562 – 576MathSciNetGoogle Scholar
  6. [GPV]
    S. Gindikin, I. Pjatecki-Shapiro, E. Vinberg, Classification and canonical realization of complex bounded homogeneous domains,Trans. Moscow Math. Soc.1963, 404 – 437Google Scholar
  7. [Vin]
    E. Vinberg, Theory of homogeneous convex cones Trudy Moskva Math. Obsc. 12 (1963) 303–358;Trans. Moscow Math. Soc.1963, 340 – 403Google Scholar

Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • R. Penney
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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