Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies

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.

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

References in corpus (1)

• Classical W-algebras in types A, B, C, D and G

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