CALOGERO-MOSER LAX PAIRS WITH SPECTRAL PARAMETER FOR GENERAL LIE-ALGEBRAS

We construct a Lax pair with spectral parameter for the elliptic Calog ero-Moser Hamiltonian systems associated with each of the finite-dimen sional Lie algebras, of the classical and of the exceptional type. Whe n the spectral parameter equals one of the three half periods of the e lliptic curve, our result for the classical Lie algebras reduces to on e of the Lax pairs without spectral parameter that were known previous ly. These Calogero-Moser systems are invariant under the Weyl group of the associated untwisted affine Lie algebra. For non-simply laced Lie algebras, we introduce new integrable systems, naturally associated w ith twisted affine Lie algebras, and construct their Lax operators wit h spectral parameter (except in the case of G(2)). (C) 1998 Published by Elsevier Science B.V.