Separation of variables in the quantum integrable models related to the Yangian $\mathcal Y[sl(3)]$

There being no precise definition of the quantum integrability, the separability of variables can serve as its practical substitute. For any quantum integrable model generated by the Yangian $\mathcal Y[sl(3)]$ the canonical coordinates and the conjugated operators are constructed which satisfy the “quantum characteristic equation” (quantum counterpart of the spectral algebraic curve for the $L$-operator. The coordinates c6nstructed provide a local separation of variables. The conditions are enlisted which are necessary for the global separation of variables to take place. Bibliography: 17 titles.