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The UC hierarchy is an extension of the KP hierarchy, which possesses notonly an infinite set of positive time evolutions but also that of negativeones. Through a similarity reduction we derive from the UC hierarchy a class ofthe Schlesinger systems including the Garnier system and the sixth Painleveequation, which describes the monodromy preserving deformations of Fuchsianlinear differential equations with certain spectral types. We also present aunified formulation of the above Schlesinger systems as a canonical Hamiltoniansystem whose Hamiltonian functions are polynomials in the canonical variables.

UC hierarchy and monodromy preserving deformation