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.