Intersection numbers in quasi-Hamiltonian reduced spaces

Jeffrey and Kirwan [15] gave expressions for intersection pairings on the reduced space of a particular Hamiltonian G-space in terms of iterated residues. The definition of quasi-Hamiltonian spaces was introduced in [1]. In [2] a localization formula for equivariant de Rham cohomolog of a compact quasi-Hamiltonian G-space was proved. In this paper we prove a residue formula for intersection pairings of reduced spaces of quasi-Hamiltonian G-spaces, by constructing a corresponding Hamiltonian G-space. Our formula is a close analogue of the result in [2]. In this article we rely heavily on the methods of [15]; for the general class of compact Lie groups G treated in [2], we rely on results of Szenes and Brion-Vergne concerning diagonal bases.