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Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies

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.

preprint2016arXivOpen access
Alberto De SoleVictor G. KacDaniele Valeri
math.RTmath-phmath.MPmath.RAnlin.SI
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Alberto De SoleVictor G. KacDaniele Valeri

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