A note on gl2 $$ \mathfrak{g}{\mathfrak{l}}_2 $$-invariant Bethe vectors

Abstract We consider gl2 $$ \mathfrak{g}{\mathfrak{l}}_2 $$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the actions of the twisted monodromy matrix entries on the twisted off-shell Bethe vectors