Integrating Schur polynomials using iterated residues at infinity

TL;DR

This paper demonstrates how to compute integrals of Schur polynomials over Lagrangian and orthogonal Grassmannians using iterated residues at infinity, providing a new computational approach in equivariant cohomology.

Contribution

It introduces a method to evaluate push-forwards in equivariant cohomology via iterated residues, connecting to classical results on Schur polynomial integrals.

Findings

Computed integrals of Schur polynomials on $LG(n)$ and $OG(n)$

Reproduced known results by Pragacz and Ratajski

Showed effectiveness of iterated residues at infinity in these calculations

Abstract

In this paper we show examples of computations achieved using the formulas of our previous paper, which express the push-forwards in equivariant cohomology as iterated residues at infinity. We consider the equivariant cohomology of the complex Lagrangian Grassmannian $LG(n)$ and the orthogonal Grassmannian with the action of the maximal torus. In particular, we show how to obtain some well-known results due to P. Pragacz and J. Ratajski on integrals of Schur polynomials over the Lagrangian Grassmannian $LG(n)$ and the orthogonal Grassmannian $OG(n)$.