Quadrilateral lattices and eigenfunction potentials for N-component KP hierarchies

The (charged) free fermion formulation of the N -component KP hierarchies is used for the description of quadrilateral lattices in terms of multicomponent KP eigenfunction potentials. Tau functions for these hierarchies are explicitly calculated, giving rise to Grammian and Casorati determinant solutions to the (discretized) Darboux or Laplace equations describing the lattices. An example of localized tau functions and eigenfunction potentials is given.