There are integrable (solvable) spin systems related to
quantum groups (quasi-triangular Hopf algebras), with
simple structure of space of states. The integrals
of motion belong to a quotient A of the braid group, which is a centralizer of the
symmetry quantum group
of the system. The space of states is a direct sum of
of tensor products of corresponding irreducible
representations of A and the quantum group.
This decomposition is multiplicity free.