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 $0$-Hecke module to each left weak Bruhat interval, called a weak Bruhat interval module. We prove that every indecomposable summand of the $0$-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.

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

Cited by in corpus (3)

• Poset modules of the $0$-Hecke algebras and related quasisymmetric power sum expansions
• Equivalence classes of lower and upper descent weak Bruhat intervals
• Quasisymmetric Schur $Q$-functions and peak Young quasisymmetric Schur functions