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


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.


Poisson Bracket Symplectic Structure Canonical Structure Extended Phase Space Zariski Open Subset 
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© 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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