Laumon Spaces and the Calogero-Sutherland Integrable System

Details Laumon Spaces and the Calogero-Sutherland Integrable System Laumon Spaces and the Calogero-Sutherland Integrable System

2008-11-26

arxiv.org/abs/0811.4454v2

Inventiones Mathematicae, Volume 178, Number 2 (Nov 2009), 299--331

Mathematics

Algebraic Geometry

31 pages. Author's Bachelor's Degree Thesis for Princeton University (advisor - Andrei Okounkov). Small changes from previous

Scientific paper

10.1007/s00222-009-0198-2

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.

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