A CONVEXITY THEOREM FOR POISSON ACTIONS OF COMPACT LIE-GROUPS

Authors
FLASCHKA H RATIU T
Citation
H. Flaschka et T. Ratiu, A CONVEXITY THEOREM FOR POISSON ACTIONS OF COMPACT LIE-GROUPS, Annales Scientifiques de l'Ecole Normale Superieure, 29(6), 1996, pp. 787-809
Citations number
18
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Annales Scientifiques de l'Ecole Normale Superieure → ACNP
ISSN journal
00129593
Volume
29
Issue
6
Year of publication
1996
Pages
787 - 809
Database
ISI
SICI code
0012-9593(1996)29:6<787:ACTFPA>2.0.ZU;2-3
Abstract
When a Poisson Lie group acts on a symplectic manifold there is a mome ntum mapping to the dual group. We prove that the image of this moment um mapping meets the positive Weyl chamber in the exponential of a con vex set. The result adapts the well-known theorem of Guillemin, Sternb erg, and Kirwan to a ''multiplicative'' (rather than ''additive'') set ting.