2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66824We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra.LaTeX2e, 8 pagesRepresentation TheoryCombinatoricstext