Bethe vectors of quantum integrable models based on Uq(gl(N))

We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by certain morphisms of the positive Borel subalgebra in Uq(gl(N)) into analogous subalgebra in Uq’(gl(N)), with q’=1/q.