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0-Hecke modules for row-strict dual immaculate functions.
- Source :
- Transactions of the American Mathematical Society; Apr2024, Vol. 377 Issue 4, p2525-2582, 58p
- Publication Year :
- 2024
-
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 immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution \psi on the ring \operatorname {QSym} of quasisymmetric functions. We give an explicit description of the effect of \psi 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 all the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 377
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 176563432
- Full Text :
- https://doi.org/10.1090/tran/9006