On Bethe vectors for the $XXZ$ model at roots of unity

We give a construction of creation operators responsible for appearance of Bethe vectors with the same eigenvalues of the transfer-matrix for the inhomogeneous arbitrary spin $XXZ$ model at roots of unity with particular quasiperiodic boundary conditions. This construction generalizes the similar one, recently obtained by K. Fabricius and B. M. McCoy, for the homogeneous six-vertex model with periodic boundary conditions. Even in the last case, the given proof for the main formulas are simpler than the original one.