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

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.

17 pages, the final version, published in Acta Math. Sinica, English series, online first, legal view-only access via http://rdcu.be/zHnI

Cited by in corpus (2)

• On the component group of a real reductive group
• Real structures on symmetric spaces