Weak Bruhat interval modules of the 0-Hecke algebra

Woo-Seok Jung, Young-Hun Kim, So-Yeon Lee, Young-Tak Oh

Published 2021-05-29Version 1

To each left weak Bruhat interval $[\sigma,\rho]_L$ we assign an $H_n(0)$-module $\mathsf{B}(\sigma,\rho)$, called the weak Bruhat interval module associated to $[\sigma,\rho]_L$. The family of weak Bruhat interval modules contains many important $H_n(0)$-modules such as projective indecomposable modules, irreducible modules, and their induced modules. We study embedding problem, induction product, restriction, and (anti-)involution twists of these modules. And, we prove that various $H_n(0)$-modules arising from the context of the quasisymmetric characteristic are decomposed into indecomposable weak Bruhat interval modules.