SYMPLECTIC ACTIONS OF COMPACT-GROUPS

For any symplectic action of a compact connected group on a compact co nnected symplectic manifold, we show that the intersection of the Weyl chamber with the image of the moment map is a closed convex polyhedro n. This extends Atiyah-Guillemin-Sternberg-Kirwan's convexity theorems to non Hamiltonian actions. As a consequence, we describe those sympl ectic actions of a torus which are coisotropic (or multiplicity free) i.e. which have at least one coisotropic orbit. (C) Academie des Scien ces/Elsevier, Paris