The Duistermaat-Heckman Measure for the Coadjoint Orbits of Compact Semisimple Lie Groups

Abstract

We apply the Guillemin-Lerman-Sternberg theorem to reprove a formula of Heckman for the Duistermaat-Heckman measure associated to the coadjoint action of $T$, a maximal torus of a compact semisimple Lie group $G$, on a regular coadjoint $G$-orbit in the dual space of the Lie algebra of $G$. This formula is, in an appropriate sense, a limiting case of the Kostant multiplicity formula.