A Littelmann-type formula for Duistermaat-Heckman measures

Given a compact Hamiltonian T-manifold M, some component of whose moment map is a Palais-Smale Morse function, we give a formula for the Duistermaat-Heckman measure (the Fourier transform of the equivariant symplectic volume) as a sum of volumes of simplices. Unlike previous formulae for this measure, this sum has only positive terms. In the case of M a flag manifold, our results are an asymptotic version of Littelmann's multiplicity result in representation theory 9]. Oblatum 5-I-1998 & 25-I-1998 / Published online: 14 October 1998