2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171147We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of \check{Q}/(h+1)\check{Q} under the Weyl group (\check{Q} being the coroot lattice and h the Coxeter number of g). From this result we deduce in a uniform way a counting formula for the ad-nilpotent ideals.AMS-TeX file, 9 pages; revised version. To appear in Journal of AlgebraRepresentation Theory17B20 (Primary); 20F55 (Secondary)text