## Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

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- by Simon Gindikin and Bernhard Krötz PDF
- Trans. Amer. Math. Soc.
**354**(2002), 3299-3327 Request permission

## Abstract:

In this paper we define a distinguished boundary for the complex crowns $\Xi \subseteq G_{\mathbb {C}} /K_{\mathbb {C}}$ of non-compact Riemannian symmetric spaces $G/K$. The basic result is that affine symmetric spaces of $G$ can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.## References

- D. N. Akhiezer and S. G. Gindikin,
*On Stein extensions of real symmetric spaces*, Math. Ann.**286**(1990), no. 1-3, 1–12. MR**1032920**, DOI 10.1007/BF01453562 - L. Barchini,
*Stein Extensions of Real Symmetric Spaces and the Geometry of the Flag Manifold*, Math. Ann., to appear. - D. Burns, S. Halverscheid, and R. Hind,
*The Geometry of Grauert Tubes and Complexification of Symmetric Spaces*, preprint. - Jacques Faraut and Adam Korányi,
*Analysis on symmetric cones*, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1994. Oxford Science Publications. MR**1446489** - L. Geatti,
*Invariant domains in the complexifiaction of a non-compcat Riemannian symmetric space*, J. Algebra, to appear. - Simon Gindikin,
*Tube domains in Stein symmetric spaces*, Positivity in Lie theory: open problems, De Gruyter Exp. Math., vol. 26, de Gruyter, Berlin, 1998, pp. 81–97. MR**1648697** - S. Gindikin, and B. Krötz,
*Invariant Stein domains in Stein symmetric spaces and a non-linear complex convexity theorem*, IMRN**18**(2002), 959–971. - S. Gindikin, B. Krötz, and G. Ólafsson,
*Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum*, MSRI preprint 2001-043. - S. Gindikin, and T. Matsuki,
*Stein Extensions of Riemann Symmetric Spaces and Dualities of Orbits on Flag Manifolds*, MSRI preprint 2001-028. - Sigurdur Helgason,
*Differential geometry, Lie groups, and symmetric spaces*, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR**514561** - Joachim Hilgert and Gestur Ólafsson,
*Causal symmetric spaces*, Perspectives in Mathematics, vol. 18, Academic Press, Inc., San Diego, CA, 1997. Geometry and harmonic analysis. MR**1407033** - Anthony W. Knapp,
*Lie groups beyond an introduction*, Progress in Mathematics, vol. 140, Birkhäuser Boston, Inc., Boston, MA, 1996. MR**1399083**, DOI 10.1007/978-1-4757-2453-0 - Bernhard Krötz and Karl-Hermann Neeb,
*On hyperbolic cones and mixed symmetric spaces*, J. Lie Theory**6**(1996), no. 1, 69–146. MR**1406006** - B. Krötz, and R. J. Stanton,
*Holomorphic extensions of representations: (I) automorphic functions*, preprint. - B. Krötz, and R. J. Stanton,
*Holomorphic extensions of representations: (II) geometry and harmonic analysis*, preprint.

## Additional Information

**Simon Gindikin**- Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
- MR Author ID: 190961
- Email: gindikin@math.rutgers.edu
**Bernhard Krötz**- Affiliation: The Ohio State University, Department of Mathematics, 231 West 18th Avenue, Columbus, Ohio 43210-1174
- Email: kroetz@math.ohio-state.edu
- Received by editor(s): November 2, 2001
- Published electronically: April 3, 2002
- Additional Notes: The first author was supported in part by NSF-grant DMS-0097314 and the MSRI

The second author was supported in part by NSF-grant DMS-0070816 and the MSRI - © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 3299-3327 - MSC (2000): Primary 22E46
- DOI: https://doi.org/10.1090/S0002-9947-02-03012-X
- MathSciNet review: 1897401