  Sato theory provides a correspondence between solutions to the KP hierarchy
and points in an infinite dimensional Grassmannian. In this correspondence,
flows generated infinitesimally by powers of the ``shift'' operator give time
dependence to the first coordinate of an arbitrarily selected point, making it
a tau-function. These tau-functions satisfy a number of integrable equations,
including the Hirota Bilinear Difference Equation (HBDE). Here, we rederive the
HBDE as a statement about linear maps between Grassmannians. In addition to
illustrating the fundamental nature of this equation in the standard theory, we
make use of this geometric interpretation of the HBDE to answer the question of
what other infinitesimal generators could be used for similarly creating
tau-functions. The answer to this question involves a ``rank one condition'',
tying this investigation to the existing results on integrable systems
involving such conditions and providing an interpretation for their
significance in terms of the relationship between the HBDE and the geometry of
Grassmannians.
