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

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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.

Original languageEnglish
Pages (from-to)30-42
Number of pages13
JournalJournal of Geometry and Physics
Volume84
DOIs
Publication statusPublished - 2014

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Keywords

  • Bihamiltonian reduction
  • Dirac reduction
  • Drinfeld-Sokolov reduction
  • Slodowy slice
  • Transverse poisson structure
  • W-algebras

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

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