p̲ -reduced Multicomponent KP Hierarchy and Classical W -algebras W(glN,p̲)
01 Pubblicazione su rivista
Carpentier S., De Sole A., Kac V. G., Valeri D., van de Leur J.
ISSN: 0010-3616
For each partition p̲ 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 p̲-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,p̲), and write down explicit formulas for evolution of these generators along the commuting Hamiltonian flows.