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Canonical structure and symmetries of the Schlesinger equations

TitleCanonical structure and symmetries of the Schlesinger equations
Publication TypeJournal Article
Year of Publication2007
AuthorsDubrovin, B, Mazzocco, M
JournalComm. Math. Phys. 271 (2007) 289-373
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 ofthe 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.

URLhttp://hdl.handle.net/1963/1997
DOI10.1007/s00220-006-0165-3

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