Pushing-forward Schur classes using iterated residues at infinity

Abstract

In this paper we review the results presented during the IMPANGA 15 Conference on the author's approach to equivariant Gysin homomorphism via iterated residues at infinity, with connections to the Jeffrey–Kirwan nonabelian localization theorem in symplectic geometry. We show examples of computations using the formulas of our previous paper, which express the push-forwards in equivariant cohomology as iterated residues at infinity. As an example we consider the equivariant cohomology of the complex Lagrangian Grassmannian $LG(n)$ with the action of the maximal torus in the symplectic group $Sp(n)$. In particular, we obtain, via our methods, analogues in equivariant cohomology of some well-known results due to Pragacz and Ratajski on push-forwards of Schur classes on $LG(n)$.