Quantum Galilei group as symmetry of magnons

Inhomogeneous quantum groups are shown to be an effective algebraic tool in the study of integrable systems. The method is illustrated on the one-dimensional Heisenberg ferromagnet whose symmetry is investigated by means of the quantum Galilei group ${\mathrm{\Gamma }}_{\mathit{q}}$(1) here introduced. Both the single magnon and the s=1/2 bound states of n magnons are completely described by the algebra. Therefore, some of the results provided by the Bethe-ansatz method emerge as a natural consequence of the quantum symmetry of the discrete chain.