In this paper we investigate invariant domains in Ξ+, a distinguished
G-invariant, Stein domain in the complexification of an irreducible
Hermitian symmetric space G/K. The domain Ξ+, recently introduced by
Kr\"otz and Opdam, contains the crown domain Ξ and it is maximal with
respect to properness of the G-action. In the tube case, it also contains
S+, an invariant Stein domain arising from the compactly causal structure
of a symmetric orbit in the boundary of Ξ. We prove that the envelope of
holomorphy of an invariant domain in Ξ+, which is contained neither in
Ξ nor in S+, is univalent and coincides with Ξ+. This fact,
together with known results concerning Ξ and S+, proves the
univalence of the envelope of holomorphy of an arbitrary invariant domain in
Ξ+ and completes the classification of invariant Stein domains
therein.Comment: 24 page