Meinolf Geck and Götz Pfeiffer,
Unipotent Characters of the Chevalley Groups
Manuscripta Math. 76 (1992), 281-304.
Let be an odd prime power and be a finite Chevalley group with
root system of type . In this paper we determine the values of the
unipotent characters of , based on G.Lusztig's parametrization of
characters and on the recent work of L.Lambe and B.Srinivasan on the Green
functions for some classical groups. We emphazise the role of the computer
MAPLE for computations in
the Weyl group and symbolic calculations with characters. The results will
then be applied to answer some questions concerning the modular
representation theory of . In particular, we show that the unique
cuspidal unipotent character of remains irreducible as -modular
Brauer character, for all primes not dividing .