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@misc{faucris.121422884,
abstract = {We consider a connected compact Lie group *K* acting on a symplectic manifold *M* such that a moment map *m* exists. A pull-back function via *m* Poisson commutes with all *K*-invariants. Guillemin-Sternberg raised the problem to find a converse. In this paper, we solve this problem by determining the Poisson commutant of the algebra of *K*-invariants. It is completely controlled by the image of *m* and a certain subquotient *W*_{M} of the Weyl group of *K*. The group *W*_{M} is also a reflection group and forms a symplectic analogue of the little Weyl group of a symmetric space. The proof rests ultimately on techniques from algebraic geometry. In fact, a major part of the paper is of independent interest: it establishes connectivity and reducedness properties of the fibers of the (complex algebraic) moment map of a complex cotangent bundle.},
author = {Knop, Friedrich},
faupublication = {no},
peerreviewed = {automatic},
title = {{Weyl} groups of {Hamiltonian} manifolds, {I}},
year = {1997}
}