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TMF, 2015, Volume 185, Number 3, Pages 527–544 (Mi tmf8894)  

This article is cited in 6 scientific papers (total in 6 papers)

Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras

O. K. Sheinman

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: Based on $\mathbb Z$-gradings of semisimple Lie algebras and invariant polynomials on them, we construct hierarchies of Lax equations with a spectral parameter on a Riemann surface and prove the commutativity of the corresponding flows.

Keywords: Lax operator algebra, Lax equation, hierarchy, semisimple Lie algebra, Riemann surface

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/tmf8894

Full text: PDF file (588 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 185:3, 1816–1831

Bibliographic databases:

Document Type: Article
Received: 19.02.2015

Citation: O. K. Sheinman, “Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras”, TMF, 185:3 (2015), 527–544; Theoret. and Math. Phys., 185:3 (2015), 1816–1831

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  • http://mi.mathnet.ru/eng/tmf/v185/i3/p527

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846  mathnet  mathscinet  zmath  elib
    2. O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. O. K. Sheinman, “Matrix divisors on Riemann surfaces and Lax operator algebras”, Trans. Moscow Math. Soc., 78 (2017), 109–121  mathnet  crossref  elib
    5. O. K. Sheinman, “Certain Reductions of Hitchin Systems of Rank 2 and Genera 2 and 3”, Dokl. Math., 97:2 (2018), 144–146  mathnet  mathnet  crossref  zmath  isi  scopus
    6. Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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