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

2009/11/11 by Dinar, Yassir
#35D45 #37K10 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.0911.2116

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.

Related

• Algebraic classical W-algebras and Frobenius manifolds
• One dimensional representations of finite W-algebras, Dirac reduction and the orbit method
• Structures of (supersymmetric) classical W-algebras
• Generalized Drinfeld-Sokolov Hierarchies and W-Algebras
• Finite and Infinite W Algebras and their Applications