Shifted Yangians and finite W-algebras

Abstract

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.

48 pages. Some notational changes, Corollary 11.11 added. To appear in Advances in Math

References in corpus (1)

• Parabolic presentations of the Yangian Y(gl_n)

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• Dirac operators and the Very Strange Formula for Lie superalgebras
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• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Multiplicative slices, relativistic Toda and shifted quantum affine algebras
• Universal filtered quantizations of nilpotent Slodowy slices