  The UC hierarchy is an extension of the KP hierarchy, which possesses not
only an infinite set of positive time evolutions but also that of negative
ones. Through a similarity reduction we derive from the UC hierarchy a class of
the Schlesinger systems including the Garnier system and the sixth Painleve
equation, which describes the monodromy preserving deformations of Fuchsian
linear differential equations with certain spectral types. We also present a
unified formulation of the above Schlesinger systems as a canonical Hamiltonian
system whose Hamiltonian functions are polynomials in the canonical variables.
