论文标题
简单代数组的不可还原表示中几乎循环的常规元素
Almost cyclic regular elements in irreducible representations of simple algebraic groups
论文作者
论文摘要
让$ g $是一个简单的线性代数组，该组在代数封闭的特征$ p \ geq 0 $上定义，让$ ϕ $为$ p $限制的不可约为$ g $。令$ t $为$ g $的最大圆环，而$ s \ in t $。我们说，如果$α（s）\neβ（s）$对于所有不同的$ t $ roots $α$和$ g $的$β$，则$ s $非常规。我们的主要结果指出，如果除$ ϕ（s）$的特征值之一以外的所有内容都具有多重性1，那么，除了一些指定的例外，$ S $是非常规的。这可以看作是我们较早结果的扩展，称在相同的假设下，$ s $必须是常规的，所有非零的权重为$ ϕ $。
Let $G$ be a simple linear algebraic group defined over an algebraically closed field of characteristic $p\geq 0$ and let $ϕ$ be a $p$-restricted irreducible representation of $G$. Let $T$ be a maximal torus of $G$ and $s\in T$. We say that $s$ is strongly regular if $α(s)\neβ(s)$ for all distinct $T$-roots $α$ and $β$ of $G$. Our main result states that if all but one of the eigenvalues of $ϕ(s)$ are of multiplicity 1 then, with a few specified exceptions, $s$ is strongly regular. This can be viewed as an extension of our earlier result saying that under the same hypotheses, $s$ must be regular and all non-zero weights of $ϕ$ are of multiplicity 1.
