Bethe vectors and recurrence relations for twisted Yangian based models

We study Olshanski twisted Yangian based models, known as one-dimensional “soliton non-preserving” open spin chains, by means of algebraic Bethe Ansatz. The even case, when the bulk symmetry is gl _2n and the boundary symmetry is sp _2n or so _2n, was studied in [12]. In the present work, we focus on the odd case, when the bulk symmetry is gl ₂n+1 and the boundary symmetry is so ₂n+1. We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and Y(gl _n)-type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.