M ay 2 00 1 Separation of variables for the A 3 elliptic Calogero - Moser system

We consider the classical elliptic Calogero-Moser model. A set of canonical separated variables for this model has been constructed in [1]. However, the generating function of the separating canonical transform is known only for two-and three-particle cases [1]. We construct this generating function for the next A 3 case as the limit of the conjectured form of the quantum separating operator. We show explicitly that this generating function gives a canonical transform from the set of original variables to the separated ones.