Knop F (1997)
Publication Language: English
Publication Type: Other publication type, arXiv
Publication year: 1997
Publisher: arXiv
Open Access Link: http://arxiv.org/abs/dg-ga/9712010
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 WM of the Weyl group of K. The group WM 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.
APA:
Knop, F. (1997). Weyl groups of Hamiltonian manifolds, I. arXiv.
MLA:
Knop, Friedrich. Weyl groups of Hamiltonian manifolds, I. arXiv, 1997.
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