论文标题
微小的嵌入
Minuscule embeddings
论文作者
论文摘要
我们研究了具有以下属性的简单线性代数组的嵌入$ j \ rightarrow g $：$ j $模块lie（$ g $）/lie（$ j $）的简单组件都是$ j $的缩影表示。当组$ g $具有两个不同长度的根和$ j $的一个子组是长根生成的子组时，就会发生一个例子。当$ j = sl_2 $和$ j = sl_3 $时，我们对所有这些嵌入式进行了分类，显示每个嵌入方式意味着在Lie的分级组件（$ G $）上存在非凡的代数结构（$ G $），并将这些结构的属性与某些$ G $的各种扭曲形式的存在与某些相对根系相关联。
We study embeddings $J \rightarrow G$ of simple linear algebraic groups with the following property: the simple components of the $J$ module Lie($G$)/Lie($J$) are all minuscule representations of $J$. One family of examples occurs when the group $G$ has roots of two different lengths and $J$ is the subgroup generated by the long roots. We classify all such embeddings when $J = SL_2$ and $J = SL_3$, show how each embedding implies the existence of exceptional algebraic structures on the graded components of Lie($G$), and relate properties of those structures to the existence of various twisted forms of $G$ with certain relative root systems.
