A combinatorial $\mathfrak{sl}_2$-action and the Sperner property for the weak order
Combinatorics
2020-01-06 v2 Representation Theory
Abstract
We construct a simple combinatorially-defined representation of which respects the order structure of the weak order on the symmetric group. This is used to resolve a conjecture of Stanley that the weak order has the strong Sperner property, and is therefore a Peck poset.
Keywords
Cite
@article{arxiv.1811.05501,
title = {A combinatorial $\mathfrak{sl}_2$-action and the Sperner property for the weak order},
author = {Christian Gaetz and Yibo Gao},
journal= {arXiv preprint arXiv:1811.05501},
year = {2020}
}
Comments
6 pages; v2: added conjecture and updated references