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.
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.
This publication is cited in the following 18 articles:
E. Trunina, A. Zotov, “Lax equations for relativistic GL(NM,C) Gaudin models on elliptic curve”, J. Phys. A, 55:39 (2022), 395202–31
K. Atalikov, A. Zotov, “Field theory generalizations of two-body Calogero–Moser models in the form of Landau–Lifshitz equations”, J. Geom. Phys., 2021, 104161–14
M. Vasilyev, A. Zotov, “On factorized Lax pairs for classical many-body integrable systems”, Rev. Math. Phys., 31:6 (2019), 1930002–45
Oleg Chalykh, “Quantum Lax Pairs via Dunkl and Cherednik Operators”, Commun. Math. Phys., 369:1 (2019), 261
A. Grekov, I. Sechin, A. Zotov, “Generalized model of interacting integrable tops”, JHEP, 2019:10 (2019), 81–33
A. V. Zotov, “Calogero–Moser model and R-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770
A. Grekov, A. Zotov, “On R-matrix valued Lax pairs for Calogero–Moser models”, J. Phys. A, 51 (2018), 315202–26
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”, Theoret. and Math. Phys., 188:2 (2016), 1121–1154
Andrey Levin, Mikhail Olshanetsky, Andrei Zotov, “Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation”, J. Phys. A, 49:39 (2016), 395202–26
A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423
Alexei Morozov, Andrey Smirnov, “Towards the Proof of AGT Relations with the Help of the Generalized Jack Polynomials”, Lett Math Phys, 104:5 (2014), 585
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118
A. Gorsky, A. Zabrodin, A. Zotov, “Spectrum of quantum transfer matrices via classical many-body systems”, JHEP, 2014, no. 1, 70–28
G. Aminov, S. Arthamonov, A. Smirnov, A. Zotov, “Rational top and its classical r-matrix”, J. Phys. A, 47:30 (2014), 305207–19
G. Aminov, A. Mironov, A. Morozov, A. Zotov, “Three-particle integrable systems with elliptic dependence on momenta and theta function identities”, Phys. Lett. B, 726:4 (2013), 802–808
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes of SL(N,C)-bundles and quantum dynamical elliptic R-matrices”, J. Phys. A, 46:3 (2013), 35201–25
A. V. Zotov, A. V. Smirnov, “Modifications of bundles, elliptic integrable systems, and related problems”, Theoret. and Math. Phys., 177:1 (2013), 1281–1338
A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov, “Characteristic classes and Hitchin systems. General construction”, Comm. Math. Phys., 316:1 (2012), 1–44
Contact us: