English

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