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arXiv · 2409.00709

The skew immaculate Hecke poset and 0-Hecke modules

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

The immaculate Hecke poset was introduced and investigated by Niese, Sundaram, van Willigenburg, Vega and Wang, who established the full poset structure, and determined modules for the 0-Hecke algebra action on immaculate and row-strict immaculate tableaux. In this paper, we extend their results by introducing the skew immaculate Hecke poset. We investigate the poset structure, and construct modules for the 0-Hecke algebra action on skew immaculate and skew row-strict immaculate tableaux, thus showing that the skew immaculate Hecke poset captures representation-theoretic information analogous to the immaculate Hecke poset. We also describe branching rules for the resulting skew modules.

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Nadia Lafrenière, Rosa Orellana, Anna Pun, Sheila Sundaram, Stephanie van Willigenburg, Tamsen Whitehead McGinley. 2024-09-01. The skew immaculate Hecke poset and 0-Hecke modules. https://doi.org/10.37236/13350

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