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arXiv · 1704.06097

Orbits of real semisimple Lie groups on real loci of complex symmetric spaces

Stéphanie Cupit-Foutou·Dmitry A. Timashev
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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 $G(\mathbb{R})$ acts on $X(\mathbb{R})$ with finitely many orbits. We describe these orbits in combinatorial terms using Galois cohomology, thus providing a patch to a result of A.Borel and L.Ji.

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Stéphanie Cupit-Foutou, Dmitry A. Timashev. 2017-04-20. Orbits of real semisimple Lie groups on real loci of complex symmetric spaces. https://doi.org/10.1007/s10114-017-7184-1

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