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On the values of unipotent characters of finite Chevalley groups of type \(E_7\) in characteristic 2. (English) Zbl 1511.20051

Summary: 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 \(E_7\).

MSC:

20C33 Representations of finite groups of Lie type
20D06 Simple groups: alternating groups and groups of Lie type
20G40 Linear algebraic groups over finite fields

Software:

CHEVIE
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Full Text: arXiv Link

References:

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