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Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 177–190 (Mi aa1191)  

This article is cited in 20 scientific papers (total in 20 papers)

Research Papers

Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\frak{gl}_N$

E. Mukhina, V. Tarasovba, A. Varchenkoc

a Department of Mathematical Sciences, Indiana University — Purdue University Indianapolis, Indianapolis, IN, USA
b St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
c Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

Abstract: It is shown that the Gaudin Hamiltonians $H_1,…,H_n$ generate the Bethe algebra of the $n$-fold tensor power of the vector representation of $\frak{gl}_N$. Surprisingly, the formula for the generators of the Bethe algebra in terms of the Gaudin Hamiltonians does not depend on $N$. Moreover, this formula coincides with Wilson's formula for the stationary Baker–Akhiezer function on the adelic Grassmannian.

Keywords: Gaudin model, Bethe algebra, Calogero–Moser space.

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English version:
St. Petersburg Mathematical Journal, 2011, 22:3, 463–472

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Received: 15.11.2009

Citation: E. Mukhin, V. Tarasov, A. Varchenko, “Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\frak{gl}_N$”, Algebra i Analiz, 22:3 (2010), 177–190; St. Petersburg Math. J., 22:3 (2011), 463–472

Citation in format AMSBIB
\by E.~Mukhin, V.~Tarasov, A.~Varchenko
\paper Gaudin Hamiltonians generate the Bethe algebra of a~tensor power of the vector representation of~$\frak{gl}_N$
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 3
\pages 177--190
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 3
\pages 463--472

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    This publication is cited in the following articles:
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    3. Bulycheva K., Chen Heng-yu, Gorsky A., Koroteev P., “BPS states in omega background and integrability”, J. High Energy Phys., 2012, no. 10, 116, 46 pp.  crossref  mathscinet  isi  elib  scopus
    4. A. V. Zabrodin, “The master $T$-operator for vertex models with trigonometric $R$-matrices as a classical $\tau$-function”, Theoret. and Math. Phys., 174:1 (2013), 52–67  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., “Classical Tau-Function for Quantum Spin Chains”, J. High Energy Phys., 2013, no. 9, 064  crossref  mathscinet  zmath  isi  elib  scopus
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    10. 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
    11. 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
    12. Zabrodin A., “Quantum Gaudin Model and Classical KP Hierarchy”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012047  crossref  isi  scopus
    13. Mukhin E., Tarasov V., Varchenko A., “Bethe Algebra of Gaudin Model, Calogero–Moser Space, and Cherednik Algebra”, Int. Math. Res. Notices, 2014, no. 5, 1174–1204  crossref  mathscinet  zmath  isi  elib  scopus
    14. Pusztai B.G., “on the Classical R-Matrix Structure of the Rational Bcn Ruijsenaars-Schneider-Van Diejen System”, Nucl. Phys. B, 900 (2015), 115–146  crossref  mathscinet  zmath  isi  elib  scopus
    15. 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
    16. Pusztai B.G., Goerbe T.F., “Lax Representation of the Hyperbolic Van Diejen Dynamics With Two Coupling Parameters”, Commun. Math. Phys., 354:3 (2017), 829–864  crossref  mathscinet  zmath  isi  scopus
    17. Pusztai B.G., “Self-Duality and Scattering Map For the Hyperbolic Van Diejen Systems With Two Coupling Parameters (With An Appendix By S. Ruijsenaars)”, Commun. Math. Phys., 359:1 (2018), 1–60  crossref  mathscinet  zmath  isi  scopus
    18. White N., “The Monodromy of Real Bethe Vectors For the Gaudin Model”, J. Comb. Algebra, 2:3 (2018), 259–300  crossref  mathscinet  isi
    19. Maillet J.M., Niccoli G., “On Quantum Separation of Variables”, J. Math. Phys., 59:9, SI (2018), 091417  crossref  mathscinet  zmath  isi  scopus
    20. Maillet J.M., Niccoli G., “Complete Spectrum of Quantum Integrable Lattice Models Associated to Y (Gl(N)) By Separation of Variables”, SciPost Phys., 6:6 (2019), 071  crossref  isi
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