Reflection Groups. A Contribution to the Handbook of Algebra
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
math.RT↗
arXiv subjects
Meinolf Geck
Publications and source records attributed to Meinolf Geck.
On the Schur indices of cuspidal unipotent characters
In previous work of Gow, Ohmori, Lusztig and the author, the Schur indices of all unipotent characters of finite groups of Lie type have been explicitly determined except for six cases in groups of type $F_4$, $E_7$ and $E_8$. In this paper, we show that the Schur indices of all cuspidal unipotent characters for type $F_4$ and $E_8$ are~1, assuming that the group is defined over a field of ``good'' characteristic. This settles four out of the six open cases. For type $E_7$, we show that the Schur indices are at most~2.
math.RT↗
The Schur indices of the cuspidal unipotent characters of the finite Chevalley groups $E_7(q)$
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.
math.RT↗