Nested Bethe ansatz for `all' open spin chains with diagonal boundary conditions

Abstract

We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl()), Y(gl(|)), U_q(gl()) or U_q(gl(|)) (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 anstaz 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 fundamental representation and for some particular super-spin chains. We give the eigenvalues, Bethe equations and the form of the Bethe vectors for the corresponding models. The Bethe vectors are expressed using a trace formula.