2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113905We give a proof of the periodicity of Zamolodchikov's Y-systems in the AxA case using a novel interpretation of the system as a condition of flatness of a connection on a certain graph.14 pages. References and minor misprints correctedRepresentation TheoryPeriodicity of Y-systems and flat connectionstext