Spin calogero particles and bispectral solutions of the matrix KP hierarchy

Maarten Bergvelt; Michael Gekhtman; Alex Kasman

doi:10.1007/s11040-009-9058-y

Spin calogero particles and bispectral solutions of the matrix KP hierarchy

Maarten Bergvelt, Michael Gekhtman, Alex Kasman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Pairs of n×n matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with r×r matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case r∈=∈1, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators.

Original language	English (US)
Pages (from-to)	181-200
Number of pages	20
Journal	Mathematical Physics Analysis and Geometry
Volume	12
Issue number	2
DOIs	https://doi.org/10.1007/s11040-009-9058-y
State	Published - May 2009

Keywords

Bispectrality
Integrable systems
Non-commutative KP hierarchy
Spin generalized Calogero-Moser particle system

ASJC Scopus subject areas

Mathematical Physics
Geometry and Topology

Online availability

10.1007/s11040-009-9058-y

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abstract = "Pairs of n×n matrices whose commutator differ from the identity by a matrix of rank r are used to construct bispectral differential operators with r×r matrix coefficients satisfying the Lax equations of the Matrix KP hierarchy. Moreover, the bispectral involution on these operators has dynamical significance for the spin Calogero particles system whose phase space such pairs represent. In the case r∈=∈1, this reproduces well-known results of Wilson and others from the 1990's relating (spinless) Calogero-Moser systems to the bispectrality of (scalar) differential operators.",

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Spin calogero particles and bispectral solutions of the matrix KP hierarchy

Abstract

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