an:07239064
Zbl 7239064
Geck, Meinolf
Computing Green functions in small characteristic
EN
J. Algebra 561, 163-199 (2020)
0021-8693
2020
j
20C33 20G40
finite groups of Lie type; Green functions; character sheaves
Summary: 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 almost all cases by work of Beynon-Spaltenstein, Lusztig und Shoji. Open cases exist for groups of exceptional type \({}^2E_6, E_7, E_8\) in small characteristics. We propose a general method for dealing with these cases, which proceeds 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 \({}^2E_6, E_7\) are solved, as well as at least one particular open case in type \(E_8\).