Quiver varieties and Yangians

We prove a conjecture of Nakajima (for type A it was announced by Ginzburg and Vasserot) giving a geometric realization, via quiver varieties, of the Yangian of type ADE (and more in general of the Yangian associated to every symmetric Kac-Moody Lie algebra). As a corollary, we get that the finite-d imensional representation theory of the quantized affine algebra and that o f the Yangian coincide.