Soliton S matrices for the critical A_(N-1)^(1) chain

We compute by Bethe Ansatz both bulk and boundary hole scattering matrices for the critical A_{N-1}^(1) quantum spin chain. The bulk S matrix coincides with the soliton S matrix for the A_{N-1}^(1) Toda field theory with imaginary coupling. We verify our result for the boundary S matrix using a generalization of the Ghoshal-Zamolodchikov boundary crossing relation.