Convexity Properties of the Moment Mapping Re-examined

Author: Sjamaar R.

Source: Advances in Mathematics, Volume 138, Number 1, September 1998 , pp. 46-91(46)

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Abstract:

Consider a Hamiltonian action of a compact Lie group on a compact symplectic manifold. A theorem of Kirwan's says that the image of the momentum mapping intersects the positive Weyl chamber in a convex polytope. I present a new proof of Kirwan's theorem, which gives explicit information on how the vertices of the polytope come about and on how the shape of the polytope near any point can be read off from infinitesimal data on the manifold. It also applies to some interesting classes of noncompact or singular Hamiltonian spaces, such as cotangent bundles and complex affine varieties. Copyright 1998 Academic Press.

Language: English

Document Type: Research article

Affiliations: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey, 08540

Publication date: 1998-09-01