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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 2, Pages 185–222
DOI: https://doi.org/10.4213/tmf9005
(Mi tmf9005)
 

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

A. M. Levinab, M. A. Olshanetskyc, A. V. Zotovade

a Institute for Theoretical and Experimental Physics, Moscow, Russia
b Department of Mathematics, National Research University "Higher School of Economics", Moscow, Russia
c Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia
d Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
e Steklov Mathematical Institute of Russian Academy of Sciences
References:
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.
Funding agency Grant number
Russian Science Foundation 14-50-00150
The research of M.A. Olshanetsky was performed at the Institute for Information Transmission Problems and was supported by a grant from the Russian Science Foundation (Grant No. 14-50-00150).
Received: 14.07.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 2, Pages 1121–1154
DOI: https://doi.org/10.1134/S0040577916080018
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: 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”, TMF, 188:2 (2016), 185–222; Theoret. and Math. Phys., 188:2 (2016), 1121–1154
Citation in format AMSBIB
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\paper Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero--Moser systems, and KZB equations
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