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SIGMA, 2012, Volume 8, 072, 11 pages (Mi sigma749)  

This article is cited in 17 scientific papers (total in 17 papers)

KZ characteristic variety as the zero set of classical Calogero–Moser Hamiltonians

Evgeny Mukhina, Vitaly Tarasovab, Alexander Varchenkoc

a Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, 402 North Blackford St., Indianapolis, IN 46202-3216, USA
b St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191023, Russia
c Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA

Abstract: We discuss a relation between the characteristic variety of the KZ equations and the zero set of the classical Calogero–Moser Hamiltonians.

Keywords: Gaudin Hamiltonians; Calogero–Moser system; Wronski map.


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ArXiv: 1201.3990
MSC: 82B23; 17B80
Received: June 9, 2012; in final form October 4, 2012; Published online October 16, 2012

Citation: Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko, “KZ characteristic variety as the zero set of classical Calogero–Moser Hamiltonians”, SIGMA, 8 (2012), 072, 11 pp.

Citation in format AMSBIB
\by Evgeny Mukhin, Vitaly Tarasov, Alexander Varchenko
\paper KZ characteristic variety as the zero set of classical Calogero--Moser Hamiltonians
\jour SIGMA
\yr 2012
\vol 8
\papernumber 072
\totalpages 11

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    2. Gaiotto D., Koroteev P., “On Three Dimensional Quiver Gauge Theories and Integrability”, J. High Energy Phys., 2013, no. 5, 126  crossref  mathscinet  zmath  isi  elib  scopus
    3. Anton Zabrodin, “The Master $T$-Operator for Inhomogeneous $XXX$ Spin Chain and mKP Hierarchy”, SIGMA, 10 (2014), 006, 18 pp.  mathnet  crossref  mathscinet
    4. Alexandrov A., Leurent S., Tsuboi Z., Zabrodin A., “The Master T-Operator for the Gaudin Model and the Kp Hierarchy”, Nucl. Phys. B, 883 (2014), 173–223  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Bulycheva K., Gorsky A., “Bps States in the Omega-Background and Torus Knots”, J. High Energy Phys., 2014, no. 4, 164  crossref  mathscinet  zmath  isi  elib  scopus
    6. Gorsky A. Zabrodin A. Zotov A., “Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems”, J. High Energy Phys., 2014, no. 1, 070, 1–28  crossref  mathscinet  isi  scopus
    7. Zabrodin A., “Quantum Gaudin Model and Classical Kp Hierarchy”, Physics and mathematics of nonlinear phenomena 2013 (pmnp2013), Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012047  crossref  isi  scopus
    8. Levin A. Olshanetsky M. Zotov A., “Planck Constant as Spectral Parameter in Integrable Systems and Kzb Equations”, J. High Energy Phys., 2014, no. 10, 109  crossref  mathscinet  zmath  isi  scopus
    9. Gadde A., Gukov S., Putrov P., “Walls, Lines, and Spectral Dualities in 3D Gauge Theories”, J. High Energy Phys., 2014, no. 5, 047  crossref  mathscinet  isi  elib  scopus
    10. Alexander Varchenko, “Characteristic Variety of the Gauss-Manin Differential Equations of a Generic Parallelly Translated Arrangement”, Mathematics, 2:4 (2014), 218–231  crossref  mathscinet  zmath
    11. A Zabrodin, “Quantum Spin Chains and Integrable Many-Body Systems of Classical Mechanics”, Springer Proceedings in Physics, 163 (2015), 29–48  crossref  zmath  scopus
    12. Gorsky A., Milekhin A., “Rg-Whitham Dynamics and Complex Hamiltonian Systems”, Nucl. Phys. B, 895 (2015), 33–63  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Tsuboi Z., Zabrodin A., Zotov A., “Supersymmetric Quantum Spin Chains and Classical Integrable Systems”, J. High Energy Phys., 2015, no. 5, 086  crossref  mathscinet  isi  elib  scopus
    14. Beketov M., Liashyk A., Zabrodin A., Zotov A., “Trigonometric Version of Quantum-Classical Duality in Integrable Systems”, Nucl. Phys. B, 903 (2016), 150–163  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. A. V. Zabrodin, A. V. Zotov, A. N. Liashyk, D. S. Rudneva, “Asymmetric six-vertex model and the classical Ruijsenaars–Schneider system of particles”, Theoret. and Math. Phys., 192:2 (2017), 1141–1153  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    16. A. Zabrodin, A. Zotov, “KZ-Calogero correspondence revisited”, J. Phys. A-Math. Theor., 50:20 (2017), 205202  crossref  mathscinet  zmath  isi  scopus
    17. Grekov A., Zabrodin A., Zotov A., “Supersymmetric Extension of Qkz-Ruijsenaars Correspondence”, Nucl. Phys. B, 939 (2019), 174–190  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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