On the character tables of the finite reductive groups E₆(q)_ad and ² E₆(q)_ad

2024/03/04 by Geck, Meinolf
#FOS: Mathematics #Primary 20C33 #Representation Theory (math.RT) #secondary 20G40

paper · doi:10.48550/arxiv.2403.02434

Abstract

We show how the character tables of the groups E₆(q)_ad and ² E₆(q)_ad can be constructed, where q is a power of~2. (Partial results are also obtained for any q not divisible by~3.) This is based on previous work by Hetz, Lusztig, Malle, Mizuno and Shoji, plus computations using Michel's version of \sf CHEVIE. We also need some general results that are specific to semisimple groups which are not of simply connected type. A further crucial ingredient is the determination of the values of the unipotent characters on unipotent elements for groups of type D₄ and D₅ (in characteristic~2).

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