The Skew Immaculate Hecke Poset and 0-Hecke Modules

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...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 32; no. 2
Main Authors Lafrenière, Nadia, Orellana, Rosa, Pun, Anna, Sundaram, Sheila, Van Willigenburg, Stephanie, Whitehead McGinley, Tamsen
Format Journal Article
LanguageEnglish
Published 25.04.2025
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/13350