  We consider the exact solution of a many-body problem of spin-$s$ particles
interacting through an arbitrary U(1) invariant factorizable $S$-matrix. The
solution is based on a unified formulation of the quantum inverse scattering
method for an arbitrary $(2s+1)$-dimensional monodromy matrix. The respective
eigenstates are shown to be given in terms of $2s$ creation fields by a general
new recurrence relation. This allows us to derive the spectrum and the
respective Bethe ansatz equations.
