Ad-nilpotent ideals of a Borel subalgebra: generators and duality
| dc.creator | Panyushev, Dmitri I. | |
| dc.date | 2003-03-09 | |
| dc.date.accessioned | 2026-07-07T04:55:53Z | |
| dc.date.available | 2026-07-07T04:55:53Z | |
| dc.description | It was shown by Cellini and Papi that an ad-nilpotent ideal determines certain element of the affine Weyl group, and that there is a bijection between the ad-nilpotent ideals and the integral points of a simplex with rational vertices. We give a description of the generators of ad-nilpotent ideals in terms of these elements, and show that an ideal has $k$ generators if and only it lies on the face of this simplex of codimension $k$. We also consider two combinatorial statistics on the set of ad-nilpotent ideals: the number of simple roots in the ideal and the number of generators. Considering the first statistic reveals some relations with the theory of clusters (Fomin-Zelevinsky). The distribution of the second statistic suggests that there should exist a natural involution (duality) on the set of ad-nilpotent ideals. Such an involution is constructed for the series A,B,C. | |
| dc.description | LaTeX2e, 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0303107 | |
| dc.identifier | http://arxiv.org/abs/math/0303107 | |
| dc.identifier | J. Algebra 274 (2004), 822-846 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66737 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | Ad-nilpotent ideals of a Borel subalgebra: generators and duality | |
| dc.type | text |