  Models generalizing the su(2) XX spin-chain were recently introduced. These
XXC models also have an underlying su(2) structure. Their construction method
is shown to generalize to the chains based on the fundamental representations
of the A_m Lie algebras. Integrability of the new models is shown in the
context of the quantum inverse scattering method. Their R-matrix is found and
shown to yield a representation of the Hecke algebra. The diagonalization of
the transfer matrices is carried out using the algebraic Bethe Ansatz. I
comment on eventual generalizations and possible links to reaction-diffusion
processes.
