On the Schur indices of cuspidal unipotent characters

Details On the Schur indices of cuspidal unipotent characters On the Schur indices of cuspidal unipotent characters

2003-06-18

arxiv.org/abs/math/0306267v1

Mathematics

Representation Theory

17 pages

Scientific paper

In previous work of Gow, Ohmori, Lusztig and the author, the Schur indices of all unipotent characters of finite groups of Lie type have been explicitly determined except for six cases in groups of type $F_4$, $E_7$ and $E_8$. In this paper, we show that the Schur indices of all cuspidal unipotent characters for type $F_4$ and $E_8$ are~1, assuming that the group is defined over a field of ``good'' characteristic. This settles four out of the six open cases. For type $E_7$, we show that the Schur indices are at most~2.

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