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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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.
  • 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.
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Additional Information
  • Simon Gindikin
  • Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
  • MR Author ID: 190961
  • Email:
  • Bernhard Krötz
  • Affiliation: The Ohio State University, Department of Mathematics, 231 West 18th Avenue, Columbus, Ohio 43210-1174
  • Email:
  • 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:
  • MathSciNet review: 1897401