论文标题
正交和杰出组的$ w_0 $的$ w_0 $
Action of $w_0$ on $V^L$ for orthogonal and exceptional groups
论文作者
论文摘要
在本说明中，我们提出了一些结果，可以部分回答以下问题。让$ g $成为一个简单的真实谎言组；什么是$ g $的$ v $ $ v $，其中最长的元素$ w_0 $ w_0 $ w_0 $ w_0 $ w $ w $在子空间$ v^l $ of $ v $ of $ l $不变的vectors的子空间$ v^l $上，这是$ l $，是$ g $的最大分配圆环的集中器？我们对该问题给出了一个猜想的答案，以及在$ g $是正交组（$ \ operatatorName {so} _n（\ Mathbb {c}）$的实际形式的实验结果（对于某些$ n $）或一个杰出的组时，我们就会给出了这种猜想的实验结果。
In this note, we present some results that partially answer the following question. Let $G$ be a simple real Lie group; what is the set of representations $V$ of $G$ in which the longest element $w_0$ of the restricted Weyl group $W$ acts nontrivially on the subspace $V^L$ of $V$ formed by vectors that are invariant by $L$, the centralizer of a maximal split torus of $G$? We give a conjectural answer to that question, as well as the experimental results that back this conjecture, when $G$ is either an orthogonal group (real form of $\operatorname{SO}_n(\mathbb{C})$ for some $n$) or an exceptional group.
