Geodesic
Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 185-222

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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. 
A. M. Levin; M. A. Olshanetsky; A. V. Zotov. Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 185-222. http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a0/
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     title = {Geometry of {Higgs} bundles over elliptic curves related to automorphisms of simple {Lie} algebras, {Calogero{\textendash}Moser} systems, and {KZB} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {188},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a0/}
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