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
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.