arXiv:nlin/0209040

Abstract. A study of fully discretized lattice equations associated
with the KdV hierarchy is presented. Loop group methods give a
systematic way of constructing discretizations of the equations
in the hierarchy. The lattice KdV system of Nijhoff et al arises
from the lowest order discretization of the trivial, lowest order
equation in the hierarchy, *b _{t}=b_{x}*.
Two new discretizations are also given, the lowest order discretization
of the first nontrivial equation in the hierarchy, and a `second order'
discretization of