Isotropy summands and Einstein Equation of Invariant Metrics on   Classical Flag Manifolds
  It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to a algebraic system, if $g$ is a $G$-invariant metric. In this paper we described this system for all flag manifolds of a classical Lie group. We also determined the number of isotropy summands for all of these spaces and proved certain properties of the set of t-roots for flag manifolds of type $B_n$, $C_n$ and $D_n$. 
Luciana Aparecida Alves and Neiton Pereira da Silva
math.DG