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Communications in Mathematical Physics

, Volume 271, Issue 2, pp 289–373 | Cite as

Canonical Structure and Symmetries of the Schlesinger Equations

  • Boris DubrovinEmail author
  • Marta Mazzocco
Article

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.

Keywords

Poisson Bracket Symplectic Structure Canonical Structure Extended Phase Space Zariski Open Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.SISSAInternational School of Advanced StudiesTriesteItaly
  2. 2.School of MathematicsThe University of ManchesterManchesterUnited Kingdom

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