Cohomology pairings on the symplectic reduction of products

Abstract

Let M be the product of two compact Hamiltonian T-spaces X and Y. We present a formula for evaluating integrals on the symplectic reduction of M by the diagonal T action. At every regular value of the moment map for X x Y, the integral is the convolution of two distributions associated to the symplectic reductions of X by T and of Y by T. Several examples illustrate the computational strength of this relationship. We also prove a linear analogue which can be used to find cohomology pairings on toric orbifolds.