A class of gradings of simple Lie algebras

Details A class of gradings of simple Lie algebras A class of gradings of simple Lie algebras

2006-05-11

arxiv.org/abs/math/0605295v1

Cont. Math. 442 (2007), AMS, 3-15

Mathematics

Representation Theory

13 pages. To appear in the Proceedings of the Conference on Lie Algebras, Vertex Operator Algebras and Their Applications

Scientific paper

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.

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