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We give a geometric construction of the phase space of the elliptic Calogero-Moser system
for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on
the -th power of the elliptic curve, where is the rank of the root system. The
Poisson structure and the Hamiltonians of the integrable system are given natural
constructions. We also exhibit a curious duality between the spectral varieties for the
system associated to a root system, and the Lagrangian varieties for...
We study the geometry of -bundles—locally projective -modules—on algebraic curves, and apply them to the study of integrable hierarchies, specifically the multicomponent
Kadomtsev–Petviashvili (KP) and spin Calogero–Moser (CM) hierarchies. We show that KP hierarchies have a geometric description as flows on moduli spaces of -bundles; in particular, we
prove that the local structure of -bundles is captured by the full Sato Grassmannian. The rational, trigonometric, and elliptic solutions of KP...
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