A Compact Imbedding of Semisimple Symmetric Spaces

Abstract

A realization of a $\ep$-family of semisimple symmetric spaces $\{G/H_\ep\}$ in a compact real analytic manifold $\X$ is constructed. The realization $\X$ has the following properties: a) The action of $G$ on $\X$ is real analytic; b) There exist open $G$-orbits that are isomorphic to $G/H_\ep$ for each signature of roots $\ep$; c) The system $\Cal M_λ$ of invariant differential equations on $G/H_\ep$ extends analytically on $\X$ and has regular singularities in the weak sense along the boundaries.