Yangian Doubles and off-Shell Bethe Vectors

Off-shell Bethe vectors for a generic $\text{fg}$ invariant integrable model are constructed through the currents of the Yangian doubles of the classical series. These off-shell Bethe vectors are shown to satisfy the defining properties which were used in \cite{LPR-RR} to prove the rectangular recurrence relations and verify the eigenvalue property of the on-shell Bethe vectors in $\text{ggo}$-invariant integrable models.