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arXiv · 1909.03301

p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p)

Sylvain Carpentier·Alberto De Sole·Victor G. Kac·Daniele Valeri·Johan van de Leur
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Abstract

For each partition p of an integer N \geq 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(gl_N,p), and write down explicit formulas for evolution of these generators along the Hamiltonian flows.

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Sylvain Carpentier, Alberto De Sole, Victor G. Kac, Daniele Valeri, Johan van de Leur. 2019-09-07. p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_N,p). https://doi.org/10.1007/s00220-020-03817-x

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