ARTICLE

Inventiones mathematicae

, Volume 135, Issue 1, pp 185-200

First online:

A Littelmann-type formula for Duistermaat-Heckman measures

  • Allen KnutsonAffiliated withDepartment of Mathematics, Brandeis University, Waltam, MA 02154-9110, USA (e-mail: allenk@alumni.caltech.edu)

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Abstract.

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].