Invariant Domains in the Complexification of a Noncompact Riemannian Symmetric Space

Let G/K be a noncompact Riemannian symmetric space and let G /K be its complexification. Then G acts on G /K by left translations. We study the invariant CR-structure of the closed G-orbits of maximal dimension and determine which ones can lie in the boundary of an invariant Stein domain. In this way, we obtain information on the G-invariant Stein domains in G /K .