TY - JOUR T1 - Canonical structure and symmetries of the Schlesinger equations JF - Comm. Math. Phys. 271 (2007) 289-373 Y1 - 2007 A1 - Boris Dubrovin A1 - Marta Mazzocco AB - 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. UR - http://hdl.handle.net/1963/1997 U1 - 2199 U2 - Mathematics U3 - Mathematical Physics ER -