Weak Bruhat interval modules of the 0-Hecke algebra

Weak Bruhat interval modules of the 0-Hecke algebra

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 \...

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Veröffentlicht in:arXiv.org 2022-05
Hauptverfasser: Jung, Woo-Seok, Kim, Young-Hun, Lee, So-Yeon, Oh, Young-Tak
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description 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.
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title Weak Bruhat interval modules of the 0-Hecke algebra
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