Graded Lie algebras, representation theory, integrable mappings and systems. Non-abelian case

The exactly integrable systems connected with a semisimple series A for arb itrary grading are presented in an explicit form. Their general solutions a re expressed in terms of the matrix elements of various fundamental represe ntations of the A, groups. The simplest example of such systems is the gene ralized Toda chain with matrices of arbitrary dimensions in each point of t he lattice. (C) 1999 Published by Elsevier Science B.V.