%0 Journal Article
%T The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups $E_7(q)$
%A Meinolf Geck
%J Mathematics
%D 2003
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0306268v1