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.
p̲ -reduced Multicomponent KP Hierarchy and Classical W -algebras W(glN,p̲) / Carpentier, S.; De Sole, A.; Kac, V. G.; Valeri, D.; van de Leur, J.. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 380:2(2020), pp. 655-722. [10.1007/s00220-020-03817-x]
p̲ -reduced Multicomponent KP Hierarchy and Classical W -algebras W(glN,p̲)
De Sole A.;Valeri D.;
2020
Abstract
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.| File | Dimensione | Formato | |
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Carpentier_postprint_p-Reduced_2020.pdf
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