The nested Bethe ansatz for 'all' open spin chains with diagonal boundary conditions

We present in a unified and detailed way the nested Bethe ansatz for open spin chains based on (super)algebras, with arbitrary representations (i.e., 'spins') on each site of the chain and diagonal boundary matrices (K+(u), K-(u)). The nested Bethe ansatz applies for a general K-(u), but a particular form of the K+(u) matrix. The construction extends and unifies the results already obtained for open spin chains based on the fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the explicit form of the Bethe vectors for the corresponding models. The Bethe vectors are also expressed using a trace formula