Separating Coordinates for the Generalized Hitchin Systems and the Classical r-Matrices
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We exhibit natural Darboux coordinates for the generalized Hitchin systems studied by Bottacin and Markman. These systems are defined on spaces of stable pairs consisting of a vector bundle and a form-valued meromorphic endomorphism of the bundle. In special cases (genus zero, genus one), the bundles are rigid and one has the rational, trigonometric and elliptic Gaudin systems. Explicit formulae are given in these cases.
KeywordsVector Bundle Genus Zero Stable Pair Hitchin System Gaudin System
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