Separation of variables for Hitchin systems with the structure group \(\text{SO}(4)\) on genus 2 curves

DOI10.1134/S0081543824020172MaRDI QIDQ6633161

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Publication date: 5 November 2024

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

exact solutionsJacobi inversion problemHitchin systemsstructure group \(\text{SO}(4)\)

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Applications of Lie algebras and superalgebras to integrable systems (17B80) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions (37J38) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Cites Work

• Stable bundles and integrable systems
• On the Hitchin system
• Riemann surfaces, separation of variables and classical and quantum integrability
• Theta functions on Riemann surfaces
• Vector bundles and Lax equations on algebraic curves
• Spectral curves of the hyperelliptic Hitchin systems
• Hitchin systems on hyperelliptic curves
• Integrable systems of algebraic origin and separation of variables
• Hitchin systems at low genera
• Theta functions and non-linear equations
• Separation of variables for type Hitchin systems on a hyperelliptic curve
• Hilbert schemes, separated variables, and \(D\)-branes

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