  We find new solutions to the Yang--Baxter equation in terms of the
intertwiner matrix for semi-cyclic representations of the quantum group
$U_q(s\ell(2))$ with $q= e^{2\pi i/N}$. These intertwiners serve to define the
Boltzmann weights of a lattice model, which shares some similarities with the
chiral Potts model. An alternative interpretation of these Boltzmann weights is
as scattering matrices of solitonic structures whose kinematics is entirely
governed by the quantum group. Finally, we consider the limit $N\to\infty$
where we find an infinite--dimensional representation of the braid group, which
may give rise to an invariant of knots and links.
