Weyl groups of Hamiltonian manifolds, I

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

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 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.

Authors with CRIS profile

Friedrich Knop Lehrstuhl für Mathematik (Algebra und Geometrie)

How to cite

APA:

Knop, F. (1997). Weyl groups of Hamiltonian manifolds, I. arXiv.

MLA:

Knop, Friedrich. Weyl groups of Hamiltonian manifolds, I. arXiv, 1997.

BibTeX: Download