Séminaire Lotharingien de Combinatoire, 86B.6 (2022), 12 pp.
Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg, Julianne Vega, Shiyun Wang
Row-Strict Dual Immaculate Functions
and 0-Hecke Modules
Abstract.
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 dual immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution ψ on the ring Qsym 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).
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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