Weyl Groups of Hamiltonian Manifolds , I

  title={Weyl Groups of Hamiltonian Manifolds , I},
  author={Friedrich Knop},
Let K be a compact connected Lie group and M a compact Hamiltonian K-manifold, i.e., a symplectic K-manifold equipped with a moment map μ : M → k. In this paper, we determine Col(M): the set of all functions on M which Poisson commute with all Kinvariant functions. For this, we construct a finite reflection group WM and show that Col(M) is completely determined by μ(M) and WM . More precisely, from μ(M) and WM we construct a topological space Y equipped with a differentiable structure (in fact… CONTINUE READING

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