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Acta Mathematica Sinica, English Series

, Volume 34, Issue 3, pp 439–453 | Cite as

Orbits of Real Semisimple Lie Groups on Real Loci of Complex Symmetric Spaces

  • Stéphanie Cupit-Foutou
  • Dmitry A. Timashev
Article

Abstract

Let G be a complex semisimple algebraic group and X be a complex symmetric homogeneous G-variety. Assume that both G, X as well as the G-action on X are defined over real numbers. Then G(ℝ) acts on X(ℝ) with finitely many orbits. We describe these orbits in combinatorial terms using Galois cohomology, thus providing a patch to a result of Borel and Ji.

Keywords

Semisimple group symmetric space real point orbit Galois cohomology 

MR(2010) Subject Classification

14M27 14G05 11E72 20G10 

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Notes

Acknowledgements

This work was initiated during Dmitry Timashev’s visit to the Ruhr University of Bochum in July 2016. The second author thanks the Transformation Groups Research team of Bochum for its hospitality and providing excellent working conditions. Both authors are grateful to Peter Heinzner for his support. Many thanks are due to the referee for helpful comments and suggestions aimed at improving the presentation.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.Faculty of Mechanics and Mathematics, Department of Higher AlgebraLomonosov Moscow State UniversityMoscowRussia

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