论文标题
通用线性超组的Weyl模块的Jantzen过滤
Jantzen filtration of Weyl modules for general linear supergroups
论文作者
论文摘要
令$ g = gl（m | n）$为代数封闭的奇数特征$ p $的一般线性超级组$ k $。在本文中，当$λ$是KAC定义的典型重量时，我们构建Weyl模块的Jantzen过滤$ V（λ）$ $ g $，因此获得了其字符的总和公式。通过Steinberg的Tensor Product定理，我们足以研究典型的权重，目的是制定不可还原字符。作为一个应用程序，事实证明，当且仅当$λ$是$ p $ typical时，就可以将不可约$ g $ -Module $ l（λ）$实现为KAC模块。
Let $G=GL(m|n)$ be a general linear supergroup over an algebraically closed field $k$ of odd characteristic $p$. In this paper we construct Jantzen filtration of Weyl modules $V(λ)$ of $G$ when $λ$ is a typical weight in the sense of Kac's definition, and consequently obtain a sum formula for their characters. By Steinberg's tensor product theorem, it is enough for us to study typical weights with aim to formulate irreducible characters. As an application, it turns out that an irreducible $G$-module $L(λ)$ can be realized as a Kac module if and only if $λ$ is $p$-typical.
