Laumon Spaces and the Calogero-Sutherland Integrable System
Algebraic Geometry
2009-11-25 v2
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.
Cite
@article{arxiv.0811.4454,
title = {Laumon Spaces and the Calogero-Sutherland Integrable System},
author = {Andrei Negut},
journal= {arXiv preprint arXiv:0811.4454},
year = {2009}
}
Comments
31 pages. Author's Bachelor's Degree Thesis for Princeton University (advisor - Andrei Okounkov). Small changes from previous version. To appear in Inventiones Mathematicae