Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces
| dc.creator | Panyushev, Dmitri I. | |
| dc.date | 2003-04-24 | |
| dc.date.accessioned | 2026-07-07T04:57:20Z | |
| dc.date.available | 2026-07-07T04:57:20Z | |
| dc.description | Let $\be$ be a Borel subalgebra of a complex simple Lie algebra $\g$. An ideal of $\be$ is called ad-nilpotent, if it is contained in $[\be,\be]$. The generators of an ad-nilpotent ideal give rise to an antichain in the poset of positive roots, and the whole theory can be expressed in a combinatorial fashion, in terms of antichains. The aim of this paper is to present a refinement of the enumerative theory of ad-nilpotent ideals for the case in which $\g$ has roots of different length. An antichain is called short, if it consists of short roots. We obtain, for short antichains, analogues of all results known for the usual antichains. | |
| dc.description | LaTeX2e, 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0304380 | |
| dc.identifier | http://arxiv.org/abs/math/0304380 | |
| dc.identifier | Europ. J. Combinatorics, 25 (2004), 93--112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67231 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Short antichains in root systems, semi-Catalan arrangements, and B-stable subspaces | |
| dc.type | text |