  We give a presentation for the finite W-algebra associated to a nilpotent
matrix inside the general linear Lie algebra over C. In the special case that
the nilpotent matrix consists of n Jordan blocks each of the same size l, the
presentation is that of the Yangian of level l associated to the Lie algebra
gl_n, as was first observed by Ragoucy and Sorba. In the general case, we are
lead to introduce some generalizations of the Yangian which we call the shifted
Yangians.
