The skew immaculate Hecke poset and 0-Hecke modules
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908523162501120 |
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| author | Lafrenière, Nadia Orellana, Rosa Pun, Anna Sundaram, Sheila van Willigenburg, Stephanie McGinley, Tamsen Whitehead |
| author_facet | Lafrenière, Nadia Orellana, Rosa Pun, Anna Sundaram, Sheila van Willigenburg, Stephanie McGinley, Tamsen Whitehead |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The skew immaculate Hecke poset and 0-Hecke modules Lafrenière, Nadia Orellana, Rosa Pun, Anna Sundaram, Sheila van Willigenburg, Stephanie McGinley, Tamsen Whitehead Representation Theory Combinatorics 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. |
| title | The skew immaculate Hecke poset and 0-Hecke modules |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2409.00709 |