Calogero-Moser systems for simple Lie groups and characteristic classes of bundles
type: Item
instance of: scholarly article
title: Calogero-Moser systems for simple Lie groups and characteristic classes of bundles
zbMATH Open document ID: 1261.37031
author: A. Zotov
author: A. Levin
author: M. Olshanetsky
author: A. Smirnov
published in: Journal of Geometry and Physics
publication date: 2012-07-04T00:00:00Z
review text: This article is a continuation of the previous article [\textit{A. Levin} et al., Commun. Math. Phys. 316, No. 1, 1--44 (2012; Zbl 1252.30029)]. The modified Calogero-Moser (CM) systems corresponding to the Higgs bundles with an arbitrary characteristic class over elliptic curves, \(\mathbb{C}/(\mathbb{Z}+\mathbb{Z}\tau)\), are considered. The characteristic class is a generalization of the Stiefel-Whitney class for the orthogonal groups and these systems are generalization of the standard Calogero-Moser systems with spin related to simple Lie groups and contain CM subsystems related to some (unbroken) subalgebras. For all algebras, the authors construct a special basis, corresponding to non-trivial characteristic lasses, the explicit forms of Lax operators and quadratic Hamiltonians. As by product, the moduli space of stable holomorphic bundles over elliptic curves with arbitrary characteristic classes is described. This article handles \(\mathrm{SL}(n, \mathbb{C})\), \(\mathrm{SO}(n)\), \(\mathrm{Sp}(n)\) \(\mathrm{Spin}(n)\), \(\mathrm{E}_6\), and \(\mathrm{E}_7\) which are basically listed in Table 1 in the previous work.
reviewed by: Shigeki Matsutani
Mathematics Subject Classification ID: 37K30
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 32L10
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 6052802
zbMATH Keywords: elliptic integrable systems
zbMATH Keywords: holomorphic bundles
zbMATH Keywords: characteristic classes
MaRDI profile type: Publication
full work available at URL: j.geomphys.2012.03.012
OpenAlex ID: W1983473286
Wikidata QID: Q115353213
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DOI: 10.1016/J.GEOMPHYS.2012.03.012
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description: scientific article; zbMATH DE number 6052802