00899nas a2200109 4500008004300000245006800043210006800111520053400179100002000713700002000733856003600753 2007 en_Ud 00aCanonical structure and symmetries of the Schlesinger equations0 aCanonical structure and symmetries of the Schlesinger equations3 aThe 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.1 aDubrovin, Boris1 aMazzocco, Marta uhttp://hdl.handle.net/1963/1997