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

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.

LaTeX, 19 pages

References in corpus (6)

• Multi-soliton solutions of the two-dimensional matrix Davey-Stewartson equation
• The solution of the N=(0|2) superconformal f-Toda lattice
• Two-dimensional Ultra-Toda integrable mappings and chains (Abelian case)
• Exactly integrable systems connected to semisimple algebras of second rank A_2, B_2, C_2, G_2
• Graded Lie algebras, representation theory, integrable mappings and systems
• The exactly integrable systems connected with semisimple algebras of the second rank $A_2,B_2,C_2,G_2$

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• W-algebras for non-abelian Toda systems
• UV manifold and integrable systems in spaces of arbitrary dimension