Speaker: Jonas Hetz (Stuttgart)
Title: On the Values of Unipotent Characters of Finite Chevalley Groups of Type \(E_6\) in characteristic 3
Abstract:
Let \(G\) be a finite Chevalley group. We are concerned with computing the values of the unipotent (complex) characters of \(G\) by making use of Lusztig's theory of character sheaves. In this setting, one has to find the transformation between several bases for the class functions on \(G\). In principle, this has been achieved by Lusztig and Shoji, but the underlying process involves some scalars which are still unknown in many cases. As an example, we shall look at the specific case where \(G\) is one of the groups \(E_6(q)\), \({{}^2}E_6(q)\), and \(q\) is a power of the bad prime \(p=3\) for \(E_6\).