The geometry of Calogero-Moser systems

Nous donnons une construction geometrique de l'espace de phase du systeme de Calogero-Moser elliptique, pour des systemes de racines arbitraires, comme espace de paires (fibres, champs de Higgs) sur la r-ieme puissance de la courbe elliptique, ou r est le rang du syteme de racines. La structure de Poisson ainsi que les Hamiltoniens ont alors des constructions geometriques naturelles. Nous exhibons aussi une dualite surprenante entre les varietes spectrales du systeme de Calogero-Moser associe a un systeme de racines, et les varietes Lagrangiennes correspondant au systeme de racines dual. Enfin, nous montrons comment, pour le systeme A n , notre construction se reduit a une construcion connue.

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