On a second Lax structure for the Calogero-Moser system:: time-dependent constants and superintegrability

A two-parameter Lax representation for the Calogero-Moser system is studied. The associated Lax equation is a time-dependent equation that includes, as a particular case, the standard Lax representation. The corresponding integrals of motion extend, and also include as a particular case, the classical expressions of the integrals of motion obtained by Moser. Finally the relation of this two-parameter Lax representation with the superintegrability of the Calogero-Moser system is discussed. (C) 2000 Elsevier Science B.V. All rights reserved. AMS classification: 37J35; 70H06.