Geodesic
Separation of variables in the quantum integrable models related to the Yangian $\mathcal Y[sl(3)]$
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 13, Tome 205 (1993), pp. 166-178
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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. 
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E. K. Sklyanin. Separation of variables in the quantum integrable models related to the Yangian $\mathcal Y[sl(3)]$. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 13, Tome 205 (1993), pp. 166-178. http://geodesic.mathdoc.fr/item/ZNSL_1993_205_a11/