  We study a one-dimensional lattice model of interacting spinless fermions.
This model is integrable for both periodic and open boundary conditions, the
latter case includes the presence of Grassmann valued non-diagonal boundary
fields breaking the bulk U(1) symmetry of the model. Starting from the
embedding of this model into a graded Yang-Baxter algebra an infinite hierarchy
of comuting transfer matrices is constructed by means of a fusion procedure.
For certain values of the coupling constant related to anisotropies of the
underlying vertex model taken at roots of unity this hierarchy is shown to
truncate giving a finite set of functional equations for the spectrum of the
transfer matrices. For generic coupling constants the spectral problem is
formulated in terms of a TQ-equation which can be solved by Bethe ansatz
methods for periodic and diagonal open boundary conditions. Possible approaches
for the solution of the model with generic non-diagonal boundary fields are
discussed.
