论文标题
$ 0 $ -HECKE代数的模块由标准排列的构图tableaux产生
Modules of the $0$-Hecke algebra arising from standard permuted composition tableaux
论文作者
论文摘要
我们研究$ h_n（0）$ - 模块$ \ mathbf {s}^σ_α$由于Tewari和van Willigenburg，它是使用称为标准排列的构图tableaux的新组合对象构造的，并分解为环形supclules。首先，我们表明，当$ \ mathbf {s}^σ_α$不可分解时，每个直接汇总出现在其分解中都是不可塑性的，并且是特征的。其次，我们发现$ \ mathbf {s}^σ_α$的特征关系并扩展了$ \ mathbf {s}^σ_α$在准对象Schur函数方面的图像。最后，我们表明$ \ mathbf {s}^σ_α$的规范子模块作为投影不可分解的模块的同构图像。
We study the $H_n(0)$-module $\mathbf{S}^σ_α$ due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux and decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable and characterize when $\mathbf{S}^σ_α$ is indecomposable. Second, we find characteristic relations among $\mathbf{S}^σ_α$'s and expand the image of $\mathbf{S}^σ_α$ under the quasi characteristic in terms of quasisymmetric Schur functions. Finally, we show that the canonical submodule of $\mathbf{S}^σ_α$ appears as a homomorphic image of a projective indecomposable module.
