Is classification of compact isotropy irreducible homogeneous Kaehler(-Einstein) manifolds known? Here, a homogeneous space is called isotropy irreducible if the isotropy representation is irreducible.

I have browsed the book "Einstein Manifolds" by Besse, and the paper "On isotropy irreducible Riemannian manifolds" by Wang and Ziller, but I cannot find the classification under the Kaehlerian condition.