Complex crowns of Riemannian symmetric spaces and non-compactly causal symmetric spaces

Simon Gindikin and Bernhard Krötz

\def\C{\mathbb C} In this paper we define a distinguished boundary for the complex crowns $\Xi\subeq G_\C /K_\C$ of non-compact Riemannian symmetric spaces $G/K$. The basic result is that affine symmetric spaces of $G$ can appear as a component of this boundary if and only if they are non-compactly causal symmetric spaces.