ad-nilpotent ideals containing a fixed number of simple root spaces
Representation Theory
2011-07-29 v3 Combinatorics
Abstract
We give formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a Lie algebra of type B or D containing a fixed number of root spaces attached to simple roots. This result solves positively a conjecture of Panyushev (cf. D. Panyushev, ad-nilpotent ideals: generators and duality, J. of Alg., to appear) and affords a complete knowledge of the above statistics for any simple Lie algebra. We also study the restriction of the above statistics to the abelian ideals of a Borel subalgebra, obtaining uniform results for any simple Lie algebra.
Cite
@article{arxiv.math/0401090,
title = {ad-nilpotent ideals containing a fixed number of simple root spaces},
author = {Paola Cellini and Pierluigi Moseneder Frajria and Paolo Papi},
journal= {arXiv preprint arXiv:math/0401090},
year = {2011}
}
Comments
Latex, 9 page, revised and expanded version: a uniform formula for the statistics in the abelian case is provided