Duistermaat-Heckman measures for Hamiltonian groupoid actions

Abstract

Consider a source proper, source connected regular symplectic groupoid acting locally freely and effectively in a Hamiltonian way, and assume that the moment map is proper and has connected fibres. In this case there is an associated Duistermaat-Heckman measure on the quotient orbifold. We show that this measure is polynomial with respect to the natural affine measure.