Inventiones mathematicae

, Volume 135, Issue 1, pp 185–200

A Littelmann-type formula for Duistermaat-Heckman measures

  • Allen Knutson

DOI: 10.1007/s002220050283

Cite this article as:
Knutson, A. Invent math (1999) 135: 185. doi:10.1007/s002220050283


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].

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Allen Knutson
    • 1
  1. 1.Department of Mathematics, Brandeis University, Waltam, MA 02154-9110, USA (e-mail: