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A class of gradings of simple Lie algebras

By Karin Baur and Nolan Wallach


Abstract. 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 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.The first author was supported by the Freie Akademische Stiftung and by DARPA contract\ud #AFRL F49620-02-C-0010

Topics: parabolic subgroups, moment map
Publisher: Dept. of Mathematics, University of Leicester
Year: 2006
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