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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.

MSC:
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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