Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies

Alberto De Sole; Victor G. Kac; Daniele Valeri

doi:10.1007/s00220-016-2632-9

Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies

Mathematical Physics 2016-10-05 v3 math.MP Rings and Algebras Representation Theory Exactly Solvable and Integrable Systems

Authors: Alberto De Sole , Victor G. Kac , Daniele Valeri

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Abstract

We apply the new method for constructing integrable Hamiltonian hierarchies of Lax type equations developed in our previous paper, to show that all W-algebras W(gl_N,f) carry such a hierarchy. As an application, we show that all vector constrained KP hierarchies and their matrix generalizations are obtained from these hierarchies by Dirac reduction, which provides the former with a bi-Poisson structure.

Keywords

classical W-algebras gl_N integrable Hamiltonian hierarchies Lax type equations Dirac reduction KP hierarchies bi-Poisson structure

Cite

@article{arxiv.1509.06878,
  title  = {Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies},
  author = {Alberto De Sole and Victor G. Kac and Daniele Valeri},
  journal= {arXiv preprint arXiv:1509.06878},
  year   = {2016}
}

Comments

48 pages. Minor revisions and a correction to formulas (7.25) and (7.48)

Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies

Abstract

Keywords

Cite

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