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J. Geom. Phys., 2012, Volume 62, Issue 8, Pages 1810–1850 (Mi jgph4)  

Calogero–Moser systems for simple Lie groups and characteristic classes of bundles

A. Levinabc, M. Olshanetskyac, A. Smirnovad, A. Zotova

a Institute of Theoretical and Experimental Physics, Moscow, 117218, Russia
b Laboratory of Algebraic Geometry, GU-HSE, 7 Vavilova Str., Moscow, 117312, Russia
c Max Planck Institute for Mathematics, Vivatsgasse 7, Bonn, 53111, Germany
d Math. Department, Columbia University, New York, NY 10027, USA

Abstract: This paper is a continuation of our paper Levin et al. [1]. We consider Modified Calogero–Moser (CM) systems corresponding to the Higgs bundles with an arbitrary characteristic class over elliptic curves. These systems are generalization of the classical Calogero–Moser systems with spin related to simple Lie groups and contain CM subsystems related to some (unbroken) subalgebras. For all algebras we construct a special basis, corresponding to non-trivial characteristic classes, the explicit forms of Lax operators and quadratic Hamiltonians. As by product, we describe the moduli space of stable holomorphic bundles over elliptic curves with arbitrary characteristic classes.

Funding Agency Grant Number
Russian Foundation for Basic Research 09-02-00393
09-01-92437
09-01-93106
Federal Agency for Science and Innovations of Russian Federation 14.740.11.0347
Dynasty Foundation
Ministry of Education and Science of the Russian Federation MK-1646.2011.1
11.G34.31.0023
The work was supported by grants RFBR-09-02-00393, RFBR-09-01-92437-KE_a, RFBR-09-01-93106-NCNILa (A.Z. and A.S.), and by the Federal Agency for Science and Innovations of Russian Federation under contract 14.740.11.0347. The work of A.Z. was also supported by the Dynasty fund and the President fund MK-1646.2011.1. The work of A.L. was partially supported by AG Laboratory GU-HSE, RF government grant, ag. 11 11.G34.31.0023.


DOI: https://doi.org/10.1016/j.geomphys.2012.03.012


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Received: 30.12.2011
Revised: 12.03.2012
Accepted:29.03.2012
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