  We present an explicit method to perform similarity reduction of a
Riemann-Hilbert factorization problem for a homogeneous GL (N, C) loop group
and use our results to find solutions to the Painleve VI equation for N=3. The
tau function of the reduced hierarchy is shown to satisfy the sigma-form of the
Painleve VI equation. A class of tau functions of the reduced integrable
hierarchy is constructed by means of a Grassmannian formulation. These
solutions provide rational solutions of the Painleve VI equation.
