Computing Green functions in small characteristic
Abstract
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 \textit{almost} all cases by work of BeynonSpaltenstein, Lusztig und Shoji. Open cases exist for groups of exceptional type ${^2\!E}_6$, $E_7$, $E_8$ in small characteristics. We propose a general method for dealing with these cases, which procedes 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 ${^2\!E}_6$, $E_7$ are solved, as well as at least one particular open case in type $E_8$.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.06970
 Bibcode:
 2019arXiv190406970G
 Keywords:

 Mathematics  Representation Theory;
 20C33;
 20G40
 EPrint:
 29 pages