Two types of boundary conditions ('soliton preserving' and 'soliton non-preserving') are investigated for the sl(N ) and sl(M|N ) open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are classified. The symmetry and the Bethe ansatz equations are derived for each case.The general treatment for non-diagonal reflection matrices associated with the 'soliton preserving' case is worked out. The connection between the 'soliton non-preserving' boundary conditions and the twisted (super-) Yangians is also discussed.

We give a unified RTT presentation of (super)-Yangians Y (g) for g = so(n), sp(2n) and osp(m|2n).

Abstract. We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.