### Abstract

We show that the two cuspidal unipotent characters of a finite Chevalley group E-T(q) have Schur index 2, provided that q is an even power of a (sufficiently large) prime number p such that p equivalent to 1 mod 4. The proof uses a refinement of Kawanaka's generalized Gelfand-Graev representations and Some explicit Computations with the CHEVIE computer algebra system.

Original language | English |
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Pages (from-to) | 201-215 |

Number of pages | 14 |

Journal | Osaka Journal of Mathematics |

Volume | 42 |

Issue number | 1 |

Publication status | Published - 2005 |

### Keywords

- IRREDUCIBLE CHARACTERS
- REPRESENTATIONS
- SUPPORT

## Cite this

Geck, M. J. (2005). The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups $E\sb 7(q)$.

*Osaka Journal of Mathematics*,*42*(1), 201-215.