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Vector bundles and Lax equations on algebraic curves. (English) Zbl 1073.14048
Summary: The Hamiltonian theory of zero-curvature equations with spectral parameter on an arbitrary compact Riemann surface is constructed. It is shown that the equations can be seen as commuting flows of an infinite-dimensional field generalization of the Hitchin system. The field analog of the elliptic Calogero-Moser system is proposed. An explicit parameterization of Hitchin system based on the Tyurin parameters for stable holomorphic vector bundles on algebraic curves is obtained.

14H70 Relationships between algebraic curves and integrable systems
14H60 Vector bundles on curves and their moduli
33E05 Elliptic functions and integrals
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
81R12 Groups and algebras in quantum theory and relations with integrable systems
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