Long Abelian ideals
Representation Theory
2007-05-23 v1 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.math/0303222,
title = {Long Abelian ideals},
author = {Dmitri I. Panyushev},
journal= {arXiv preprint arXiv:math/0303222},
year = {2007}
}
Comments
LaTeX2e, 8 pages