  We consider an extension of the (t-U) Hubbard model taking into account new
interactions between the numbers of up and down electrons. We confine ourselves
to a one-dimensional open chain with L sites (4^L states) and derive the
effective Hamiltonian in the strong repulsion (large U) regime. This
Hamiltonian acts on 3^L states. We show that the spectrum of the latter
Hamiltonian (not the degeneracies) coincides with the spectrum of the
anisotropic Heisenberg chain (XXZ model) in the presence of a Z field (2^L
states). The wave functions of the 3^L-state system are obtained explicitly
from those of the 2^L-state system, and the degeneracies can be understood in
terms of irreducible representations of U_q(\hat{sl(2)}).
