Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems, and KZB equations

被引：0

作者：

Levin, A. M. ^{[1
,2
]}

Olshanetsky, M. A. ^{[3
]}

Zotov, A. V. ^{[2
,4
,5
]}

机构：

[1] Natl Res Univ, Dept Math, Higher Sch Econ, Moscow, Russia

[2] Inst Theoret & Expt Phys, Moscow, Russia

[3] RAS, Kharkevich Inst Informat Transmiss Problems, Moscow, Russia

[4] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

[5] Moscow Inst Phys & Technol, Dolgoprudnyi, Moscow Oblast, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2016年 / 188卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

elliptic integrable system; finite-order Lie algebra automorphism; Higgs bundle; Knizhnik-Zamolodchikov-Bernard equation; DYNAMICAL R-MATRICES; ZUMINO-WITTEN MODELS; HITCHIN SYSTEMS; OPERATORS;

D O I：

10.1134/S0040577916080018

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1121 / 1154

页数：34

共 7 条

[1] Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero–Moser systems, and KZB equations
A. M. Levin
M. A. Olshanetsky
A. V. Zotov
Theoretical and Mathematical Physics, 2016, 188 : 1121 - 1154
[2] Spin Calogero-Moser systems associated with simple Lie algebras
Li, LC
Xu, P
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 331 (01): : 55 - 60
[3] Calogero-Moser systems for simple Lie groups and characteristic classes of bundles
Levin, A.
Olshanetsky, M.
Smirnov, A.
Zotov, A.
JOURNAL OF GEOMETRY AND PHYSICS, 2012, 62 (08) : 1810 - 1850
[4] Calogero-Moser and Toda systems for twisted and untwisted affine Lie algebras
D'Hoker, E
Phong, DH
NUCLEAR PHYSICS B, 1998, 530 (03) : 611 - 640
[5] Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras
Li, Luen-Chau
Nie, Zhaohu
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2011, 308 (02) : 415 - 438
[6] Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras
Luen-Chau Li
Zhaohu Nie
Communications in Mathematical Physics, 2011, 308 : 415 - 438
[7] A Compatible System of Equations Related to the Lie Superalgebra gl(n|m) and Integrable Calogero-Moser Model
Dotsenko, E.
JETP LETTERS, 2023, 117 (04) : 317 - 319

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