2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54793A system of SU(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz. The highest weight property of the solutions is proved. (Part I of a series of articles on the generalized nested Bethe Ansatz and difference equations.)18 pages, LaTeXHigh Energy Physics - Theorytext