A Littelmann-type formula for Duistermaat-Heckman measures
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- Knutson, A. Invent math (1999) 135: 185. doi:10.1007/s002220050283
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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 .