TY - JOUR

T1 - p-reduced Multicomponent KP Hierarchy and Classical W-algebras W(gl_N,p)

AU - Carpentier, S.

AU - De Sole, A.

AU - Kac, V.G.

AU - Valeri, D.

AU - van de Leur, J.W.

PY - 2020/8/4

Y1 - 2020/8/4

N2 - 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.

AB - 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.

U2 - 10.1007/s00220-020-03817-x

DO - 10.1007/s00220-020-03817-x

M3 - Article

SN - 0010-3616

VL - 380

SP - 655

EP - 722

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

ER -