Canonical structure and symmetries of the Schlesinger equations

Boris Dubrovin, Marta Mazzocco

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The Schlesinger equations S (n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m× m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations S (n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates. © Springer-Verlag 2007.
    Original languageEnglish
    Pages (from-to)289-373
    Number of pages84
    JournalCommunications in Mathematical Physics
    Volume271
    Issue number2
    DOIs
    Publication statusPublished - Apr 2007

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