Ad-Nilpotent Ideals of a Parabolic Subalgebra
Representation Theory
2007-11-05 v2
Abstract
We extend the results of Cellini-Papi on the characterizations of nilpotent and abelian ideals of a Borel subalgebra to parabolic subalgebras of a simple Lie algebra. These characterizations are given in terms of elements of the affine Weyl group and faces of alcoves. In the case of a parabolic subalgebra of a classical Lie algebra, we give formulas for the number of these ideals.
Keywords
Cite
@article{arxiv.math/0701679,
title = {Ad-Nilpotent Ideals of a Parabolic Subalgebra},
author = {Céline Righi},
journal= {arXiv preprint arXiv:math/0701679},
year = {2007}
}
Comments
Proof of 4.1 corrected and generalized to all types. Further references and remarks added