## Osaka Journal of Mathematics

### The Schur indices of the cuspidal unipotent characters of the finite chevalley groups $E_{7}(q)$

Meinolf Geck

#### Abstract

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 \textit{CHEVIE} computer algebra system.

#### Article information

Source
Osaka J. Math., Volume 42, Number 1 (2005), 201-215.

Dates
First available in Project Euclid: 21 July 2006

Geck, Meinolf. The Schur indices of the cuspidal unipotent characters of the finite chevalley groups $E_{7}(q)$. Osaka J. Math. 42 (2005), no. 1, 201--215. https://projecteuclid.org/euclid.ojm/1153494322