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arXiv · 2509.05918

Minimal elements in the skew extended 0-Hecke poset

Nadia Lafrenière·Rosa Orellana·Anna Pun·Sheila Sundaram·Stephanie van Willigenburg·Tamsen Whitehead McGinley
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Abstract

The row-strict 0-Hecke action on standard immaculate skew tableaux was studied by the present authors, who showed that it gives rise to a bounded poset, called the \emph{skew immaculate Hecke poset}, and consequently to a cyclic 0-Hecke module. It was further shown that the subposet of skew standard extended immaculate tableaux always has a unique maximal element, but may have multiple minimal elements. In this paper we focus on these minimal elements, completely classifying them for a family of skew shapes that we call \emph{lobsters}. Moreover, we prove that when the skew shape is connected, the skew extended Hecke poset does have a unique minimal element, thereby showing that the associated 0-Hecke module is cyclic for both the row-strict and the dual immaculate actions.

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Nadia Lafrenière, Rosa Orellana, Anna Pun, Sheila Sundaram, Stephanie van Willigenburg, Tamsen Whitehead McGinley. 2025-09-09. Minimal elements in the skew extended 0-Hecke poset. https://arxiv.org/abs/2509.05918

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