p ̲ -reduced Multicomponent KP hierarchy and classical W -algebras W ( gl N , p ̲ )

Carpentier, S., De Sole, A., Kac, V. G., Valeri, D. and Van De Leur, J. (2020) p ̲ -reduced Multicomponent KP hierarchy and classical W -algebras W ( gl N , p ̲ ). Communications in Mathematical Physics, 380, pp. 655-722. (doi: 10.1007/s00220-020-03817-x)

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Abstract

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Valeri, Dr Daniele
Authors: Carpentier, S., De Sole, A., Kac, V. G., Valeri, D., and Van De Leur, J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
Publisher:Springer
ISSN:0010-3616
ISSN (Online):1432-0916
Published Online:04 August 2020
Copyright Holders:Copyright © 2020 Springer-Verlag GmbH Germany, part of Springer Nature
First Published:First published in Communications in Mathematical Physics 380:655–722
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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