Abstract
We construct a simple combinatorially-defined representation of s l 2 \mathfrak {sl}_2 which respects the order structure of the weak order on the symmetric group. This is used to prove that the weak order has the strong Sperner property, and is therefore a Peck poset, solving a problem raised by Björner [Orderings of Coxeter groups, Amer. Math. Soc., Providence, RI, 1984, pp. 175â195]; a positive answer to this question had been conjectured by Stanley [Some Schubert shenanigans, preprint, 2017].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have