  We prove a conjecture of Nakajima (for type A the result was announced by
Ginzburg- 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 tthe characters of
the simple finite dimensional representations of the quantized affine algebra
and that of the yangian coincide.
