Calogero-Moser systems for simple Lie groups and characteristic classes of bundles
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.
scientific article; zbMATH DE number 6052802
scientific article