Abstract
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 $E_7$.
Acknowledgments
I thank Meinolf Geck for many comments and hints, as well as Gunter Malle for comments on an earlier version. I also wish to thank an unknown referee for detailed suggestions on how to improve the paper. This work was supported by DFG SFB-TRR 195.
Citation
Jonas Hetz. "On the values of unipotent characters of finite Chevalley groups of type $E_7$ in characteristic 2." Osaka J. Math. 59 (3) 591 - 610, July 2022.
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