  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.
