论文标题
带有有趣等级品种的小型模块
Small modules with interesting rank varieties
论文作者
论文摘要
本文重点介绍了组模块的排名品种，而组代数$ \ mathbb {f} e $，其中$ e $是一个小学的Abelian $ p $ -group，$ p $是代数封闭的字段$ \ MATHBB {F} $的特征。在第一部分中，我们为一个不可分解的模块的绿色顶点提供了足够的条件，该模块包含一个基本的Abelian $ p $ -group $ e $，而该模块的等级限制为$ e $。在第二部分中，鉴于代数品种$ v $，我们探讨了找到一个具有等级品种$ v $的小模块的问题。特别是，我们检查了对称组$ \ mathfrak {s} _ {kp} $的简单模块$ d^{（kp-p-p+1,1^{p-1}）} $。
This paper focuses on the rank varieties for modules over a group algebra $\mathbb{F}E$ where $E$ is an elementary abelian $p$-group and $p$ is the characteristic of an algebraically closed field $\mathbb{F}$. In the first part, we give a sufficient condition for a Green vertex of an indecomposable module containing an elementary abelian $p$-group $E$ in terms of the rank variety of the module restricted to $E$. In the second part, given a homogeneous algebraic variety $V$ , we explore the problem on finding a small module with rank variety $V$ . In particular, we examine the simple module $D^{(kp-p+1,1^{p-1})}$ for the symmetric group $\mathfrak{S}_{kp}$.
