Classification of reductive real spherical pairs II. The semisimple case

Abstract

If $\mathfrak{g}$ is a real reductive Lie algebra and $\mathfrak{h}<\mathfrak{g}$ is a subalgebra, then $(\mathfrak{g},\mathfrak{h})$ is called real spherical provided that $\mathfrak{g}=\mathfrak{h}+\mathfrak{p}$ for some choice of a minimal parabolic subalgebra $\mathfrak{p}\subset \mathfrak{g}$. In this paper we classify all real spherical pairs $(\mathfrak{g},\mathfrak{h})$ where $\mathfrak{g}$ is semi-simple but not simple and $\mathfrak{h}$ is a reductive real algebraic subalgebra. The paper is based on the classification of the case where $\mathfrak{g}$ is simple (see arXiv:1609.00963) and generalizes the results of Brion and Mikityuk in the (complex) spherical case.

Extended revised version. Section 6 and Appendix B are new. To appear in Transformation Groups. 40p