Combinatorics of Vogan diagrams for almost-Kähler manifolds.

Let G be a non-compact classical semisimple Lie group and let G / V be the adjoint orbit with respect to a fixed element in G. These manifolds can be equipped with an almost-Kähler structure and we provide explicit formulae for the existence of special almost-complex structures on G / V purely in terms of the combinatorics of the associated Vogan diagram. The formulae are given separately for Lie groups whose Lie algebras are of type A ℓ , B ℓ , C ℓ , D ℓ , where ℓ denotes the rank of the Lie algebra. [ABSTRACT FROM AUTHOR]