\(q\)-KP hierarchy, bispectrality and Calogero-Moser systems
type: Item
instance of: scholarly article
title: \(q\)-KP hierarchy, bispectrality and Calogero-Moser systems
zbMATH Open document ID: 0983.37080
DOI: 10.1016/S0393-0440(00)00006-1
author: Plamen Iliev
published in: Journal of Geometry and Physics
publication date: 2001-02-05T00:00:00Z
review text: In [\textit{E. Frenkel}, Int. Math. Res. Not. 2, 55-76 (1996; Zbl 0860.17033)] the author has proposed a \(q\)-deformation of the \(N\)th KdV hierarchy which is Hamiltonian with respect to the quantum Poisson algebra. A slightly different deformation on the KP hierarchy was proposed in [\textit{L. Haine} and \textit{P. Iliev}, J. Phys. A 30, 7217-7227 (1997; Zbl 0928.35148)]. It was shown that by making an appropriate shift in the arguments of the classical Schur polynomials one obtains rational solutions of the deformed hierarchy. In the article under review the author shows that there is a one-to-one correspondece between the \(q\)-tau functions of a \(q\)-deformation of the KP hierarchy and the planes in Sato Grassmannian. On the base of this correspondence some applications to \(q\)-deformation of the Calogero-Moser hierarchy are given.
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1523514
zbMATH Keywords: KP-hierarchy
zbMATH Keywords: \(q\)-deformations
zbMATH Keywords: tau-functions
zbMATH Keywords: \(q\)-pseudo-difference operators
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1523514