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

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Book cover Topics in Geometry

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 20))

Abstract

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.

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References

  1. R Bernat et al.,Représentations des groupes de Lie résoluble, Dunod Paris, 1972

    Google Scholar 

  2. S. Dorfmeister, Quasi-symmetric Siegel domains and the automorphisms of homogeneous Siegel domains,Amer. J. Math102 (1980), 537 – 563

    Article  MathSciNet  MATH  Google Scholar 

  3. Harish-Chandra, Representations of semi-simple Lie groups, IV,Amer. J. Math.77 (1955), 743–777

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  4. S. Kaneyuki, Homogeneous Bounded Domains and Siegel Domains,Lecture Notes in Mathematics241 (1971), Springer-Verlag, Berlin

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  5. J. Koszul, Sur la forme hermitienne canonique des espaces homogenes complexes,Canad. J. Math.7 (1955), 562 – 576

    MathSciNet  Google Scholar 

  6. S. Gindikin, I. Pjatecki-Shapiro, E. Vinberg, Classification and canonical realization of complex bounded homogeneous domains,Trans. Moscow Math. Soc.1963, 404 – 437

    Google Scholar 

  7. E. Vinberg, Theory of homogeneous convex cones Trudy Moskva Math. Obsc. 12 (1963) 303–358;Trans. Moscow Math. Soc.1963, 340 – 403

    Google Scholar 

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© 1996 Birkhäuser Boston

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Penney, R. (1996). The Harish-Chandra Realization for Non-Symmetric Domains in ℂn . In: Gindikin, S. (eds) Topics in Geometry. Progress in Nonlinear Differential Equations and Their Applications, vol 20. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2432-7_11

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  • DOI: https://doi.org/10.1007/978-1-4612-2432-7_11

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-7534-3

  • Online ISBN: 978-1-4612-2432-7

  • eBook Packages: Springer Book Archive

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