On the geometry of nilpotent orbits

2004/10/02 by Wilfried Schmid, Kari Vilonen
Mathematics · #math.RT #math.AG #msc:22E45 #msc:22E47 #msc:22E60 #msc:53C30

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published as Surv. Differ. Geom., VII, Int. Press, Somerville, MA, pp. 565-623 (2000); Sir Michael Atiyah: a great mathematician of the twentieth century. Asian J. Math. 3 (1999), no. 1, 233-274

arxiv created 2004/10/02 · arxiv updated 2009/12/01

Abstract

In this paper we obtain various results about the geometry of nilpotent orbits. In particular, we obtain a better understanding of the Kostant-Sekiguchi correspondence and Kronheimer's instanton flow. We utilize the moment map of Ness and the SL(2)-orbit theorem from Hodge theory. The results of this paper are used in the proof of the Barbarsch-Vogan conjecture in math.RT/0005305 (Ann. of Math. (2) 151 (2000), no. 3, 1071-1118).

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