p-reduced Multicomponent KP Hierarchy and Classical W-algebras W(gl_N,p)

Abstract

For each partition p– of an integer N≥2, consisting of r parts, an integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently by some of us. In the present paper we show that any tau-function of the p–-reduced r-component KP hierarchy produces a solution of this integrable hierarchy. Along the way we provide an algorithm for the explicit construction of the generators of the corresponding classical W-algebra W(glN,p–), and write down explicit formulas for evolution of these generators along the commuting Hamiltonian flows.