On the Moment Map of a  Multiplicity Free Action

The purpose of this note is to show that the Orbit Conjecture of  C. Benson, J. Jenkins, R. L. Lipsman and G. Ratcliff  follows easily from  results of Guillemin-Sternberg and Brion. This conjecture characterizes multiplicity free actions in terms of some properties of moment maps.

Appeared in Coll. Math.71, 107--110 (1996)