Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-04-19
Nucl.Phys. B530 (1998) 537-610
Physics
High Energy Physics
High Energy Physics - Theory
84 pages, Plain TeX, 1 figure; minor typos corrected, 2 refs added
Scientific paper
10.1016/S0550-3213(98)00568-9
We construct a Lax pair with spectral parameter for the elliptic Calogero-Moser Hamiltonian systems associated with each of the finite dimensional Lie algebras, of the classical and of the exceptional type. When the spectral parameter equals one of the three half periods of the elliptic curve, our result for the classical Lie algebras reduces to one of the Lax pairs without spectral parameter that were known previously. 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 with twisted affine Lie algebras, and construct their Lax operators with spectral parameter (except in the case of $G_2$).
D'Hoker Eric
Phong Duong Hong
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