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TMF, 2016, Volume 188, Number 2, Pages 185–222 (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

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).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9005

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English version:
Theoretical and Mathematical Physics, 2016, 188:2, 1121–1154

Bibliographic databases:

ArXiv: 1507.04265
Received: 14.07.2015

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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