English

Weak Bruhat interval modules of the 0-Hecke algebra

Representation Theory 2022-05-25 v3 Combinatorics

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 00-Hecke module to each left weak Bruhat interval, called a weak Bruhat interval module. We prove that every indecomposable summand of the 00-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

R2 v1 2026-06-24T02:35:34.195Z