Invariant Ordering on the Simply Connected Covering of the Shilov Boundary of a Symmetric Domain

The Shilov boundary of a symmetric domain $D=G/K$ of tube type has the form $G/P$, where $P$ is a maximal parabolic subgroup of the group $G$. We prove that the simply connected covering of the Shilov boundary possesses a unique (up to inversion) invariant ordering, which is induced by the continuous invariant ordering on the simply connected covering of $G$ and can readily be described in terms of the corresponding Jordan algebra.