Weak Bruhat interval modules of the 0-Hecke algebra
Abstract
The purpose of this paper is to provide a unified method for dealing with various 0-Hecke modules constructed using tableaux so far. To do this, we assign a -Hecke module to each left weak Bruhat interval, called a weak Bruhat interval module. We prove that every indecomposable summand of the -Hecke modules categorifying dual immaculate quasisymmetric functions, extended Schur functions, quasisymmetric Schur functions, and Young row-strict quasisymmetric Schur functions is a weak Bruhat interval module. We further study embedding into the regular representation, induction product, restriction, and (anti-)involution twists of weak Bruhat interval modules.
Keywords
Cite
@article{arxiv.2105.14169,
title = {Weak Bruhat interval modules of the 0-Hecke algebra},
author = {Woo-Seok Jung and Young-Hun Kim and So-Yeon Lee and Young-Tak Oh},
journal= {arXiv preprint arXiv:2105.14169},
year = {2022}
}
Comments
36 pages; v2: abstract, introduction, Subsection 3.1, and Subsection 3.3 are revised; reference [13] is added, v3: minor typos are revised; published in Math. Z