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Graded Lie algebras, representation theory, integrable mappings, and integrable systems

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Abstract

A new class of integrable mappings and chains is introduced. The corresponding 1+2 integrable systems that are invariant under such integrable mappings are presented in an explicit form. Soliton-type solutions of these systems are constructed in terms of matrix elements of fundamental representations of semisimple An algebras for a given group element. The possibility of generalizing this construction to the multidimensional case is discussed.

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Authors and Affiliations

  1. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autònoma de Mèxico, Cuernavaca, México

    A. N. Leznov

  2. Institute for High Energy Physics, Protvino, Moscow Oblast, Russia

    A. N. Leznov

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  1. A. N. Leznov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 2, pp. 251–271, February, 2000.

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Leznov, A.N. Graded Lie algebras, representation theory, integrable mappings, and integrable systems. Theor Math Phys 122, 211–228 (2000). https://doi.org/10.1007/BF02551198

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