On orbits of antichains of positive roots
| dc.creator | Panyushev, Dmitri I. | |
| dc.date | 2007-11-21 | |
| dc.date | 2008-07-29 | |
| dc.date.accessioned | 2026-07-07T09:53:03Z | |
| dc.date.available | 2026-07-07T09:53:03Z | |
| dc.description | For any finite poset P, there is a natural operator $X$ acting on the antichains of P. We discuss conjectural properties of this operator for some graded posets associated with irreducible root systems. In particular, if $Δ^+$ is the set of positive roots and $Π$ is the set of simple roots in $Δ^+$, then we consider the cases $P=Δ^+$ and $Δ^+\setminus Π$. For the root system of type $A_n$, we consider an $X$-invariant integer-valued function on the set of antichains of $Δ^+$ and establish some properties of it. | |
| dc.description | 12 pages, final version; to appear in Europ. J. Combinatorics | |
| dc.identifier | https://arxiv.org/abs/0711.3353 | |
| dc.identifier | http://arxiv.org/abs/0711.3353 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165816 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | On orbits of antichains of positive roots | |
| dc.type | text |