  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.
