arXiv Analytics

Sign in

arXiv:1811.05501 [math.CO]AbstractReferencesReviewsResources

A combinatorial $\mathfrak{sl}_2$-action and the Sperner property for the weak order

Christian Gaetz, Yibo Gao

Published 2018-11-13Version 1

We construct a simple combinatorially-defined representation of $\mathfrak{sl}_2$ 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.

Comments: 6 pages
Categories: math.CO, math.RT
Related articles: Most relevant | Search more
arXiv:math/0411647 [math.CO] (Published 2004-11-30, updated 2005-10-21)
Asymptotics of characters of symmetric groups, genus expansion and free probability
arXiv:math/0605654 [math.CO] (Published 2006-05-24)
Constructing all irreducible Specht modules in a block of the symmetric group
arXiv:1704.00851 [math.CO] (Published 2017-04-04)
Some Schubert shenanigans

Links

Toolbox