Classification of reductive real spherical pairs. I: The simple case (Q2416405)

Let $g$ be a real reductive Lie algebra and $h \subset g$ a subalgebra. The subalgebra $h$ is called real spherical if there exists a minimal parabolic subalgebra $p \subset g$ such that $g = h + p$. The authors call $(g, h)$ a real spherical pair. \par The main result of the paper under review is a classification of non-trivial real spherical pairs for which $g$ is simple and $h$ is an algebraic and reductive subalgebra.