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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...
Let be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let be a connected complex reductive affine algebraic group equipped with a real form . We define pseudo-real principal -bundles on . These are generalizations of real algebraic principal -bundles over a real algebraic variety. Next we define stable, semistable and polystable pseudo-real principal -bundles. Their relationships with the usual stable, semistable...
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