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

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Abstract

Based on 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.

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Authors and Affiliations

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

    O. K. Sheinman

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  1. O. K. Sheinman
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Correspondence to O. K. Sheinman.

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This research was funded by a grant from the Russian Science Foundation (Project No. 14-50-00005).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 185, No. 3, pp. 527–544, December, 2015. Original article submitted February 19, 2015.

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Sheinman, O.K. Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras. Theor Math Phys 185, 1816–1831 (2015). https://doi.org/10.1007/s11232-015-0381-0

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  • DOI: https://doi.org/10.1007/s11232-015-0381-0

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