A class of gradings of simple Lie algebras
In this paper we give a classification
of parabolic subalgebras
of simple Lie algebras over $\mathbb{C}$ that satisfy
two properties. The
first property is Lynch's sufficient condition for the
vanishing of certain
Lie algebra cohomology spaces for generalized Whittaker
modules associated
with the parabolic subalgebra and the second is that the
moment map of the
cotangent bundle of the corresponding generalized flag variety
be birational
onto its image. We will call this condition the moment map
condition.
pdf-file