Computing Green functions in small characteristic

2019/04/15 by Meinolf Geck, Geck, Meinolf
Mathematics · #20C33 #20G40 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C33 #msc:20G40

paper · pdf · doi:10.48550/arxiv.1904.06970

29 pages; added one case in type E8

arxiv created 2019/04/29 · arxiv updated 2019/04/30

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 almost all cases by work of Beynon--Spaltenstein, Lusztig und Shoji. Open cases exist for groups of exceptional type ² E₆, E₇, E₈ 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 E₆, E₇ are solved, as well as at least one particular open case in type E₈.

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