2003/03/18 by Dmitri I. Panyushev
Mathematics · #math.RT #math.CO
published as Adv. in Math. 186 (2004), 307-316 · LaTeX2e, 8 pages
arxiv created 2003/03/18 · arxiv updated 2009/11/30
We 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.