Geodesic
The skew immaculate Hecke poset and 0-Hecke modules
Nadia Lafrenière ; Rosa Orellana1 ; Anna Pun2 ; Sheila Sundaram3 ; Stephanie van Willigenburg4 ; Tamsen Whitehead McGinley5
1Dartmouth College, Hanover, NH, USA
2Baruch College, New York, NY, USA
3Pierrepont School
4University of British Columbia, Vancouver, BC, Canada
5Santa Clara University, Santa Clara, CA, USA
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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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.
DOI : 10.37236/13350
Classification : 05E10, 05E05, 06A07, 20C08, 20C30
Mots-clés : row-strict dual immaculate functions

Nadia Lafrenière    ; Rosa Orellana  1   ; Anna Pun  2   ; Sheila Sundaram  3   ; Stephanie van Willigenburg  4   ; Tamsen Whitehead McGinley  5

1 Dartmouth College, Hanover, NH, USA
2 Baruch College, New York, NY, USA
3 Pierrepont School
4 University of British Columbia, Vancouver, BC, Canada
5 Santa Clara University, Santa Clara, CA, USA 
@article{10_37236_13350,
     author = {Nadia Lafreni\`ere and Rosa Orellana and Anna Pun and Sheila Sundaram and Stephanie van Willigenburg and Tamsen Whitehead McGinley},
     title = {The skew immaculate {Hecke} poset and {0-Hecke} modules},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {2},
     doi = {10.37236/13350},
     zbl = {1564.05363},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13350/}
}
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Nadia Lafrenière; Rosa Orellana; Anna Pun; Sheila Sundaram; Stephanie van Willigenburg; Tamsen Whitehead McGinley. The skew immaculate Hecke poset and 0-Hecke modules. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13350

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