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).

We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are written in an R-matrix form. In this paper we are concerned with the algebraic structure and representations of the algebra X(a). We prove an analog of the Poincaré-Birkhoff-Witt theorem for X(a) and show that the Yangian Y(a) can be realized as a subalgebra of X(a). Furthermore, we give an independent proof of the classification theorem for the finite-dimensional irreducible representations of X(a) which implies the corresponding theorem of Drinfeld for the Yangians Y(a). We also give explicit constructions for all fundamental representation of the Yangians.