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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.00708 |
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| _version_ | 1866912574890573824 |
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| author | Niese, Elizabeth Sundaram, Sheila van Willigenburg, Stephanie Vega, Julianne Wang, Shiyun |
| author_facet | Niese, Elizabeth Sundaram, Sheila van Willigenburg, Stephanie Vega, Julianne Wang, Shiyun |
| contents | We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution $ψ$ on the ring of quasisymmetric functions. We give an explicit description of the effect of $ψ$ on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles (2019).
Like the dual immaculate function, the row-strict dual immaculate function is the generating function of a suitable set of tableaux, corresponding to a specific descent set. We give a complete combinatorial and representation-theoretic picture by constructing 0-Hecke modules for the remaining variations on descent sets, and showing that \emph{all} the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00708 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | 0-Hecke modules for row-strict dual immaculate functions Niese, Elizabeth Sundaram, Sheila van Willigenburg, Stephanie Vega, Julianne Wang, Shiyun Combinatorics Representation Theory 05E05, 05E10, 06A07, 16T05, 20C08 We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution $ψ$ on the ring of quasisymmetric functions. We give an explicit description of the effect of $ψ$ on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles (2019). Like the dual immaculate function, the row-strict dual immaculate function is the generating function of a suitable set of tableaux, corresponding to a specific descent set. We give a complete combinatorial and representation-theoretic picture by constructing 0-Hecke modules for the remaining variations on descent sets, and showing that \emph{all} the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets. |
| title | 0-Hecke modules for row-strict dual immaculate functions |
| topic | Combinatorics Representation Theory 05E05, 05E10, 06A07, 16T05, 20C08 |
| url | https://arxiv.org/abs/2202.00708 |