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.Comment: 92 pages, no figures. Theorem 1.2 corrected, other misprints removed.
To appear on Comm. Math. Phy