摘要
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.
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.
基金
partially supported by the Russian Foundation for Basic Research(Grant No.16-01-00818)
