A class of gradings of simple Lie algebras

摘要

In this paper we give a classification of parabolic subalgebras of simple Lie algebras over C that satisfy two properties. The first property is Lynch's sufficient condition for the vanishing of certain Lie algebra cohomol-ogy 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.