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    Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy

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    Pairs of n×nn\times n matrices whose commutator differ from the identity by a matrix of rank rr are used to construct bispectral differential operators with r×rr\times 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=1r=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. This new class of pairs (L,Λ)(L, \Lambda) of bispectral matrix differential operators is different than those previously studied in that LL acts from the left, but Λ\Lambda from the right on a common r×rr\times r eigenmatrix.Comment: 16 page
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