The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups E7(q)
Meinolf Geck
Abstract
We show that the two cuspidal unipotent characters of a finite Chevalley group E7(q) have Schur index~2, provided that q is an even power of a (sufficiently large) prime number p such that p 1 4. The proof uses a refinement of Kawanaka's generalized Gelfand--Graev representations and some explicit computations with the CHEVIE computer algebra system.
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