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Block Toeplitz Determinants, Constrained KP and Gelfand-Dickey Hierarchies

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Abstract

We propose a method for computing any Gelfand-Dickey τ function defined on the Segal-Wilson Grassmannian manifold as the limit of block Toeplitz determinants associated to a certain class of symbols \({\cal W}(t;z)\). Also truncated block Toeplitz determinants associated to the same symbols are shown to be τ functions for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.

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  1. SISSA-International School for Advanced Studies, Via Beirut 2/4, 34014, Grignano, Italy

    M. Cafasso

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  1. M. Cafasso
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Cafasso, M. Block Toeplitz Determinants, Constrained KP and Gelfand-Dickey Hierarchies. Math Phys Anal Geom 11, 11–51 (2008). https://doi.org/10.1007/s11040-008-9038-7

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