Speaker: Jonas Hetz (Stuttgart)
Title: On the Values of Unipotent Characters of Finite Groups of Lie Type
Abstract:
Let \(G\) be a finite group of Lie type. Lusztig's theory of character sheaves gives rise to a basis \(\mathbf B\) of the class functions on \(G\). The functions in \(\mathbf B\) can, in principle, be computed. On the other hand, Lusztig conjectured an explicit base change between \(\mathbf B\) and the irreducible characters of \(G\). If this is established, we would thus essentially be in a position to determine the character table of \(G\). We shall focus on unipotent characters and, as an example, consider the specific case \(G = E_7(q)\), where \(q\) is a power of the bad prime \(p = 2\) for \(E_7\).