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

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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 185, Number 3, Pages 527–544
DOI: https://doi.org/10.4213/tmf8894 (Mi tmf8894)

This article is cited in 8 scientific papers (total in 8 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

Full-text PDF (588 kB) Citations (8)

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

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.

Received: 19.02.2015

English version:
Theoretical and Mathematical Physics, 2015, Volume 185, Issue 3, Pages 1816–1831
DOI: https://doi.org/10.1007/s11232-015-0381-0

Bibliographic databases:

Document Type: Article

Language: Russian

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

Citation in format AMSBIB

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https://www.mathnet.ru/eng/tmf/v185/i3/p527

This publication is cited in the following 8 articles:

P. I. Borisova, O. K. Sheinman, “Hitchin Systems on Hyperelliptic Curves”, Proc. Steklov Inst. Math., 311 (2020), 22–35
O. K. Sheinman, “Spectral Curves of the Hyperelliptic Hitchin Systems”, Funct. Anal. Appl., 53:4 (2019), 291–303
O. K. Sheinman, “Certain reductions of Hitchin systems of rank 2 and genera 2 and 3”, Dokl. Math., 97:2 (2018), 144–146
Elena Yu. Bunkova, “Hirzebruch functional equation: classification of solutions”, Proc. Steklov Inst. Math., 302 (2018), 33–47
O. K. Sheinman, “Matrix divisors on Riemann surfaces and Lax operator algebras”, Trans. Moscow Math. Soc., 78 (2017), 109–121
O. K. Sheinman, “Lax operator algebras and integrable systems”, Russian Math. Surveys, 71:1 (2016), 109–156
V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200
Oleg K. Sheinman, “Global current algebras and localization on Riemann surfaces”, Mosc. Math. J., 15:4 (2015), 833–846

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

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References:	53
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