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Theoretical and Mathematical Physics

, Volume 188, Issue 2, pp 1121–1154 | Cite as

Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations

  • A. M. LevinEmail author
  • M. A. Olshanetsky
  • A. V. Zotov
Article

Abstract

We construct twisted Calogero–Moser systems with spins as Hitchin systems derived from the Higgs bundles over elliptic curves, where the transition operators are defined by arbitrary finite-order automorphisms of the underlying Lie algebras. We thus obtain a spin generalization of the twisted D’Hoker–Phong and Bordner–Corrigan–Sasaki–Takasaki systems. In addition, we construct the corresponding twisted classical dynamical r-matrices and the Knizhnik–Zamolodchikov–Bernard equations related to the automorphisms of Lie algebras.

Keywords

elliptic integrable system finite-order Lie algebra automorphism Higgs bundle Knizhnik–Zamolodchikov–Bernard equation 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • A. M. Levin
    • 1
    • 2
    Email author
  • M. A. Olshanetsky
    • 3
  • A. V. Zotov
    • 1
    • 4
    • 5
  1. 1.Department of MathematicsNational Research University Higher School of EconomicsMoscowRussia
  2. 2.Institute for Theoretical and Experimental PhysicsMoscowRussia
  3. 3.Kharkevich Institute for Information Transmission ProblemsRASMoscowRussia
  4. 4.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia
  5. 5.Moscow Institute of Physics and TechnologyDolgoprudny, Moscow OblastRussia

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