小特征量下格林函数的计算
Computing Green functions in small characteristic
摘要：
设$G(q)$是域上具有$q$元素的有限Lie型群，其中$q$是素数幂.由Deligne和Lusztig定义的$G(q)$的格林函数在\textit{almost}的所有情况下都是Beynon-Spaldom、Lusztig和Shoji的工作所知的。对于特殊类型${^2\!E}_6$、$E_7$、$E_8$的小特征组，存在开放病例。我们提出了一个一般的方法来处理这些情况下，这是由减少到的情况下，$q$是一个素数，然后使用计算机代数技术。以这种方式，解决了类型${^2\!E}_6$、$E_7$中的所有未决情况以及类型$E_8$中的至少一个特定未决情况。
英文摘要：
Let $G(q)$ be a finite group of Lie type over a field with $q$ elements, where $q$ is a prime power. The Green functions of $G(q)$, as defined by Deligne and Lusztig, are known in \textit{almost} all cases by work of Beynon--Spaltenstein, Lusztig und Shoji. Open cases exist for groups of exceptional type ${^2\!E}_6$, $E_7$, $E_8$ in small characteristics. We propose a general method for dealing with these cases, which procedes by a reduction to the case where $q$ is a prime and then uses computer algebra techniques. In this way, all open cases in type ${^2\!E}_6$, $E_7$ are solved, as well as at least one particular open case in type $E_8$.
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