Limbeek–Zimmer conjecture on divisible domains in flag manifolds

Let $G/P$ be a flag manifold, where $G/P$ is neither real projective space nor the conformal sphere. A proper divisible domain is a proper domain in $G/P$ admitting a properly discontinuous cocompact action by a discrete subgroup of automorphisms. Limbeek–Zimmer's conjecture. Any proper divisible domain of $G/P$ is symmetric. This asks whether the nonsymmetric divisible domains known in real projective space can occur in other flag manifolds. The source gives no resolution of the conjecture; it notes that realizations of the noncompact dual of a Nagano space provide symmetric divisible proper domains.