Weak Bruhat interval modules of the 0-Hecke algebras for stable Grothendieck polynomials

For a partition $λ$, let $G_λ^{(β)}$ be the stable $β$-Grothendieck polynomial attached to $λ$. Each homogeneous component of the $β= 1$ specialization $G_λ^{(1)}$ is Schur-positive and hence positive in the fundamental basis of quasisymmetric functions. For $m\ge|λ|$, let $G_{λ,m}^{(1)}$ be the hom