Backlund transformations for certain rational solutions of Painleve VI

We introduce certain Backlund transformations for rational solutions of the Painleve VI equation. These transformations act on a family of Painleve VI tau functions. They are obtained from reducing the Hirota bilinear equations that describe the relation between certain points in the 3 component polynomial KP Grassmannian. In this way we obtain transformations that act on the root lattice of A(5). We also show that this A(5) root lattice can be related to the F-4((1)) root lattice. We thus obtain Backlund transformations that relate Painleve VI tau functions, parametrized by the elements of this F-4((1)) root lattice.