Classical Affine W-Algebras for \mathfrakgl_N and Associated Integrable Hamiltonian Hierarchies

2015/09/30 by Alberto De Sole, Victor G. Kac, Daniele Valeri · 1 citation
Mathematics · Physics and Astronomy · #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Dirac (video compression format) #Hamiltonian (control theory) #Hamiltonian system #Homotopy and Cohomology in Algebraic Topology #Integrable system #Lax pair #Nonlinear Waves and Solitons #R-matrix #math-ph #math.MP #math.RA #math.RT #msc:17B08 #msc:17B63 #msc:17B69 #msc:17B80 #msc:35Q53 #msc:37K10 #msc:37K30 #nlin.SI

paper · pdf · doi:10.1007/s00220-016-2632-9

published as Communications in Mathematical Physics, 2016, 348(1), 265-319 · 48 pages. Minor revisions and a correction to formulas (7.25) and (7.48)

openalex publication_date 2016/05/24 · arxiv created 2016/06/02 · openalex created_date 2016/06/24 · arxiv updated 2016/10/05 · openalex updated_date 2026/08/05

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.

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