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. 
@article{TMF_2016_188_2_a0,
     author = {A. M. Levin and M. A. Olshanetsky and A. V. Zotov},
     title = {Geometry of {Higgs} bundles over elliptic curves related to automorphisms of simple {Lie} algebras, {Calogero--Moser} systems, and {KZB} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {185--222},
     publisher = {mathdoc},
     volume = {188},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a0/}
}
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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/