τ-Functions for a two-point version of the KP-hierarchy

In this paper a multipoint version of the linearization of the KP-hierarchy is described. Solutions of this system in the form of wave functions are constructed starting from a suitable Grassmann manifold and a group of commuting flows corresponding to the configuration of n points in C. The failure of equivariance at lifting these flows to the determinant bundle over this Grassmann manifold is measured by the determinants of certain Fredholm operators, the so-called τ-functions. In the case of two points an explicit relation between these τ-functions and the wave functions is derived.