论文标题
双色完美的准对称函数的0-Hecke模块的同源性能
Homological properties of 0-Hecke modules for dual immaculate quasisymmetric functions
论文作者
论文摘要
令$ n $为非负整数。对于$ n $的每个构图$α$，berg $ \ textit {et al。} $引入了一个环状不可兼容$ h_n（0）$ - 模块$ \ mathcal {v}_α$，具有双无启示的准对象函数，作为quasissmptricmmetricmmetric特征的图像。在本文中，我们从同源观点研究$ \ Mathcal {V}_α$。确切地说，我们构建了$ \ Mathcal {v}_α$的最小投影呈现，并构建了$ \ Mathcal {V}_α$的最小注射介绍。使用它们，我们计算$ {\ rm ext}^1_ {h_n（0）}（\ Mathcal {v}_α，{\ bf f}_β）$和$ {\ rm ext}^1__ {h_n（h_n（h_n（h_n）） $ {\ bf f}_β$是附加到$ n $的构图$β$的简单$ h_n（0）$。我们还计算$ {\ rm ext} _ {h_n（0）}^i（\ Mathcal {v}_α，\ Mathcal {V}_β）$时，当$ i = 0,1 $ = 0,1 $和$β\le_lα$，其中$ \ le_l le_l $ \ le_l $代表ComporticeChications on Composectrons on Comportionssss上。
Let $n$ be a nonnegative integer. For each composition $α$ of $n$, Berg $\textit{et al.}$ introduced a cyclic indecomposable $H_n(0)$-module $\mathcal{V}_α$ with a dual immaculate quasisymmetric function as the image of the quasisymmetric characteristic. In this paper, we study $\mathcal{V}_α$'s from the homological viewpoint. To be precise, we construct a minimal projective presentation of $\mathcal{V}_α$ and a minimal injective presentation of $\mathcal{V}_α$ as well. Using them, we compute ${\rm Ext}^1_{H_n(0)}(\mathcal{V}_α, {\bf F}_β)$ and ${\rm Ext}^1_{H_n(0)}( {\bf F}_β, \mathcal{V}_α)$, where ${\bf F}_β$ is the simple $H_n(0)$-module attached to a composition $β$ of $n$. We also compute ${\rm Ext}_{H_n(0)}^i(\mathcal{V}_α,\mathcal{V}_β)$ when $i=0,1$ and $β\le_l α$, where $\le_l$ represents the lexicographic order on compositions.
