2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66707This paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a Borel subalgebra. Our main result is a nice uniform formula for the dimension of maximal ideals in these posets. We also obtain results on ad-nilpotent ideals which complete the analysis started in \cite{CP2}, \cite{CP3}.AmsTex file, 38 pages; revised version. To appear in Advances in Mathematics under the title "Abelian ideals of Borel subalgebras and affine Weyl groups"Representation Theorytext