Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry

We present a nested algebraic Bethe ansatz for a one-dimensional open spin chain whose boundary quantum spaces are irreducible so _{2 n} - or sp _{2 n} -representations, and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian Y ^± (gl _{2 n} ). We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so _{2 n} - or sp _{2 n} -symmetric open spin chain to that of a gl _n -symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations.