Weyl groups of Hamiltonian manifolds, I
| dc.creator | Knop, Friedrich | |
| dc.date | 1997-12-20 | |
| dc.date.accessioned | 2026-07-07T03:24:37Z | |
| dc.date.available | 2026-07-07T03:24:37Z | |
| dc.description | 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. | |
| dc.description | 33 pages, TeX | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9712010 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9712010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33401 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58F05, 57S15, 14L30 | |
| dc.title | Weyl groups of Hamiltonian manifolds, I | |
| dc.type | text |