The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups $E_7(q)$

Details The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups $E_7(q)$ The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups $E_7(q)$

2003-06-18

arxiv.org/abs/math/0306268v1

Mathematics

Representation Theory

12 pages

Scientific paper

We show that the two cuspidal unipotent characters of a finite Chevalley
group $E_7(q)$ have Schur index~2, provided that $q$ is an even power of a
(sufficiently large) prime number $p$ such that $p\equiv 1 \bmod 4$. The proof
uses a refinement of Kawanaka's generalized Gelfand--Graev representations and
some explicit computations with the {\sf CHEVIE} computer algebra system.

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