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Graded Lie algebras, representation theory, integrable mappings and systems: nonabelian case

A. N. Leznov
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Abstract

The exactly integrable systems connected with semisimple series $A$ for arbitrary grading are presented in explicit form. Their general solutions are expressed in terms of the matrix elements of various fundamental representations of $A_n$ groups. The simplest example of such systems is the generalized Toda chain with the matrices of arbitrary dimensions in each point of the lattice.

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A. N. Leznov. 1998-10-08. Graded Lie algebras, representation theory, integrable mappings and systems: nonabelian case. https://doi.org/10.1016/s0550-3213(99)80001-7

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