Algebraic Solution of the Hubbard Model on the Innnite Interval

We develop the quantum inverse scattering method for the one-dimensional Hubbard model on the innnite line at zero density. This enables us to diagonalize the Hamiltonian algebraically. The eigenstates can be classiied as scattering states of particles, bound pairs of particles and bound states of pairs. We obtain the corresponding creation and annihilation operators and calculate the S-matrix. The Hamiltonian on the innnite line is invariant under the Yangian quantum group Y(su(2)). We show that the n-particle scattering states transform like n-fold tensor products of fundamental representations of Y(su(2)) and that the bound states are Yangian singlet. z