2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58206A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in terms of matrix elements of fundamental representations of semisimple $A_n$ algebras for a given group element. The possibility of generalizing this construction to multi-dimensional case is discussed.LaTeX, 20 pagesMathematical PhysicsHigh Energy Physics - TheoryExactly Solvable and Integrable Systemstext