$W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

Yassir Dinar

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arXiv · 0911.2116

$W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions

Yassir Dinar

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Abstract

We prove that the classical $W$-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical $W$-algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. In addition, using this result we prove again that the transverse Poisson structure to a nilpotent orbit is polynomial and we better clarify the relation between classical and finite $W$-algebras.

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BibTeX RIS

Yassir Dinar. 2009-11-11. $W$-algebras and the equivalence of bihamiltonian, Drinfeld-Sokolov and Dirac reductions. https://arxiv.org/abs/0911.2116

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