Japanese Journal of Mathematics

, Volume 2, Issue 2, pp 303–311 | Cite as

Corner view on the crown domain

Original Article

Abstract.

In this paper we raise a question about the boundary of the crown domain of a Riemannian symmetric space X. In case X is of Hermitian type we give an affirmative answer.

Keywords and phrases:

complex crown Hermitian Lie group semi-simple Lie group non-compactly causal space Shilov boundary 

Mathematics Subject Classification (2000):

22E10 22E15 32M15 

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References

  1. 1.
    D. Akhiezer and S. Gindikin, On Stein extensions of real symmetric spaces, Math. Ann., 286 (1990), 1–12.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Math. Monogr., Oxford Univ. Press, New York, 1994.MATHGoogle Scholar
  3. 3.
    S. Gindikin and B. Krötz, Complex crowns of Riemannian symmetric spaces and noncompactly causal symmeyric spaces, Trans. Amer. Math. Soc., 354 (2002), 3299–3327.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    S. Gindikin, B. Krötz and G. Ólafsson, Holomorphic H-spherical distribution vectors in principal series representations, Invent. Math., 158 (2004), 643–682.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    J. Hilgert and G. Ólafsson, Causal Symmetric Spaces. Geometry and Harmonic Analysis, Perspect. Math., 18, Academic Press, 1997.Google Scholar
  6. 6.
    B. Krötz, Domains of holomorphy for irreducible unitary representations of simple Lie groups, Preprint (2006). http://www.mpim-bonn.mpg.de/preprints/send?bid=3070
  7. 7.
    B. Krötz, Crown theory for the upper half-plane, To appear in Contemp. Math. http://www.mpim-bonn.mpg.de/preprints/send?bid=3296
  8. 8.
    B. Krötz and E. M. Opdam, Analysis on the crown domain, To appear in Geom. Funct. Anal. http://www.mpim-bonn.mpg.de/preprints/send?bid=3007
  9. 9.
    B. Krötz and R. J. Stanton, Holomorphic extensions of representations. II. Geometry and harmonic analysis, Geom. Funct. Anal., 15 (2005), 190–245.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© The Mathematical Society of Japan and Springer 2007

Authors and Affiliations

  1. 1.Max-Planck-Institut für MathematikBonnDeutschland

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