论文标题
关于特征$ e_7 $类型的有限chevalley群体的单位字符的值2
On the values of unipotent characters of finite Chevalley groups of type $E_7$ in characteristic 2
论文作者
论文摘要
令$ g $为有限的谎言类型。为了确定$ g $的角色表，卢斯蒂格（Lusztig）开发了角色束带的理论。在此框架中，必须在$ g $上找到两个基础函数的两个基础之间的转换，其中一个是$ g $的不可减至的字符，另一个由与角色滑轮相关的特征函数组成。原则上，这是由Lusztig和Shoji实现的，但是基本过程涉及一些标量，这些标量在许多情况下仍然是未知的。指定这些标量的问题可以简化为考虑尖齿轮束。对于$ g = e_7（q）$，而$ q $的特定情况，我们将处理后者，而$ e_7 $是糟糕的prime $ p = 2 $的功率。
Let $G$ be a finite group of Lie type. In order to determine the character table of $G$, Lusztig developed the theory of character sheaves. In this framework, one has to find the transformation between two bases for the space of class functions on $G$, one of them being the irreducible characters of $G$, the other one consisting of characteristic functions associated to character sheaves. In principle, this has been achieved by Lusztig and Shoji, but the underlying process involves some scalars which are still unknown in many cases. The problem of specifying these scalars can be reduced to considering cuspidal character sheaves. We will deal with the latter for the specific case where $G=E_7(q)$, and $q$ is a power of the bad prime $p=2$ for $E_7$.
