Shifted Yangians and Finite W -algebras

  title={Shifted Yangians and Finite W -algebras},
  author={Alexander Kleshchev},
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 gln, 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. 
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