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 -