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Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

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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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Authors and Affiliations

  1. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Maarten Bergvelt

  2. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Michael Gekhtman

  3. Department of Mathematics, College of Charleston, Charleston, SC, 29424, USA

    Alex Kasman

Authors
  1. Maarten Bergvelt
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  2. Michael Gekhtman
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  3. Alex Kasman
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Correspondence to Alex Kasman.

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Bergvelt, M., Gekhtman, M. & Kasman, A. Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy. Math Phys Anal Geom 12, 181–200 (2009). https://doi.org/10.1007/s11040-009-9058-y

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  • DOI: https://doi.org/10.1007/s11040-009-9058-y

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