Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

0-Hecke modules for row-strict dual immaculate functions
HTML articles powered by AMS MathViewer

by Elizabeth Niese, Sheila Sundaram, Stephanie van Willigenburg, Julianne Vega and Shiyun Wang
Trans. Amer. Math. Soc. 377 (2024), 2525-2582
DOI: https://doi.org/10.1090/tran/9006
Published electronically: February 9, 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.

References
Similar Articles
Bibliographic Information
  • Elizabeth Niese
  • Affiliation: Marshall University, Huntington, West Virginia 25755
  • MR Author ID: 927796
  • Email: elizabeth.niese@gmail.edu, niese@marshall.edu
  • Sheila Sundaram
  • Affiliation: Pierrepont School, Westport, Connecticut 06880; and School of Mathematics University of Minnesota, Minneapolis, Minnesota 55455
  • MR Author ID: 271955
  • ORCID: 0000-0002-1583-4740
  • Email: shsund@comcast.net
  • Stephanie van Willigenburg
  • Affiliation: University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
  • MR Author ID: 619047
  • ORCID: 0000-0002-5340-5568
  • Email: steph@math.ubc.ca
  • Julianne Vega
  • Affiliation: Kennesaw State University, Kennesaw, Georgia 30144
  • MR Author ID: 1408962
  • Email: jvega@maret.org
  • Shiyun Wang
  • Affiliation: University of Southern California, Los Angeles, California 90089-2532
  • MR Author ID: 1526691
  • Email: shiyunwa@usc.edu
  • Received by editor(s): February 28, 2022
  • Received by editor(s) in revised form: June 5, 2023
  • Published electronically: February 9, 2024
  • Additional Notes: Sheila Sundaram is the corresponding author
    The third author was supported in part by the National Sciences Research Council of Canada.
  • © Copyright 2024 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 377 (2024), 2525-2582
  • MSC (2020): Primary 05E05, 05E10, 06A07, 16T05, 20C08
  • DOI: https://doi.org/10.1090/tran/9006