Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains

We present a nested algebraic Bethe ansatz for one-dimensional so 2n- and sp 2n-symmetric open spin chains with diagonal boundary conditions. The monodromy matrix of these spin chains satisfies the defining relations on the extended twisted Yangians X ρ(so 2n,so 2n ρ) tw and X ρ(sp 2n,sp 2n ρ) tw, respectively. We use a generalisation of the De Vega and Karowski approach allowing us to relate the spectral problem of so 2n- or sp 2n-symmetric open spin chain to that of gl n-symmetric open spin chain studied by Belliard and Ragoucy. We explicitly derive the structure of Bethe vectors, their eigenvalues and the nested Bethe equations. We also provide a proof of Belliard and Ragoucy's trace formula for Bethe vectors of gl n-symmetric open spin chains.