UC hierarchy, monodromy preserving deformation and hypergeometric function

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, the UC hierarchy yields a broad class of
Schlesinger systems including (higher order) Painleve VI and Garnier
systems, which describe monodromy preserving deformations of Fuchsian
linear differential equations with certain spectral types.
The above class of Schlesinger systems has interesting features as
polynomial Hamiltonian structure, Weyl group symmetry, algebraic
solutions, hypergeometric solutions, etc.