%0 Journal Article
%D 2014
%T Adler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras
%A Alberto De Sole
%A Victor G. Kac
%A Daniele Valeri
%X We put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy.
%I SISSA
%G eng
%U http://hdl.handle.net/1963/7242