Laumon Spaces and the Calogero-Sutherland Integrable System

TL;DR

This paper proves Braverman's conjecture linking Laumon quasiflag spaces' generating functions to Calogero-Sutherland eigenfunctions, advancing understanding of geometric representation theory and integrable systems.

Contribution

It provides a proof that the generating function of equivariant Chern polynomial integrals on Laumon spaces matches the Calogero-Sutherland eigenfunction, confirming a significant conjecture.

Findings

Proof of Braverman's conjecture established

Generating function Z(m) identified as Calogero-Sutherland eigenfunction

Advances connection between geometric spaces and integrable systems

Abstract

This paper contains a proof of a conjecture of Braverman concerning Laumon quasiflag spaces. We consider the generating function Z(m), whose coefficients are the integrals of the equivariant Chern polynomial (with variable m) of the tangent bundles of the Laumon spaces. We prove Braverman's conjecture, which states that Z(m) coincides with the eigenfunction of the Calogero-Sutherland hamiltonian, up to a simple factor which we specify. This conjecture was inspired by the work of Nekrasov in the affine \hat{sl}_n setting, where a similar conjecture is still open.