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.
Categories: math.RT