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arXiv · 1811.05501

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

Christian Gaetz·Yibo Gao
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Abstract

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.

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Christian Gaetz, Yibo Gao. 2020-01-03. A combinatorial $\mathfrak{sl}_2$-action and the Sperner property for the weak order. https://doi.org/10.1090/proc%2F14655

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