  We study a model of assisted diffusion of hard-core particles on a line. The
model shows strongly ergodicity breaking : configuration space breaks up into
an exponentially large number of disconnected sectors. We determine this
sector-decomposion exactly. Within each sector the model is reducible to the
simple exclusion process, and is thus equivalent to the Heisenberg model and is
fully integrable. We discuss additional symmetries of the equivalent quantum
Hamiltonian which relate observables in different sectors. In some sectors, the
long-time decay of correlation functions is qualitatively different from that
of the simple exclusion process. These decays in different sectors are deduced
from an exact mapping to a model of the diffusion of hard-core random walkers
with conserved spins, and are also verified numerically. We also discuss some
implications of the existence of an infinity of conservation laws for a
hydrodynamic description.
