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Convexity properties of the moment mapping. III. (English) Zbl 0561.58016
This paper is concerned with the moment mappings associated to compact Lie group actions on compact symplectic manifolds, which are functions from the manifolds to the duals of the Lie algebras of the groups acting on them. In Part I and II by V. Guillemin and S. Sternberg [ibid. 67, 491-513 (1982; Zbl 0503.58017) and ibid. 77, 533-546 (1984; see the paper reviewed above)] it is proved that the intersection of the image of a moment map with any Weyl chamber is a convex polytope in the cases when either the group is a torus or the manifold is Kähler. Guillemin and Sternberg conjectured that the same is true in general. The purpose of this paper is to prove their conjecture.

MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
53D50 Geometric quantization
53C80 Applications of global differential geometry to the sciences
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References:
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