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The 1D Heisenberg spin chain with anisotropy of the XXZ type is analyzed interms of the symmetry given by the quantum Galilei group Gamma_q(1). We showthat the magnon excitations and the s=1/2, n-magnon bound states are determinedby the algebra. Thus the Gamma_q(1) symmetry provides a description thatnaturally induces the Bethe Ansatz. The recurrence relations determined byGamma_q(1) permit to express the energy of the n-magnon bound states in aclosed form in terms of Tchebischeff polynomials.Comment: (pag. 10

Heisenberg XXZ model and quantum Galilei group