  In the literature on finite groups of Lie type, there exist two different
conventions about the labelling of the irreducible characters of Weyl groups of
type~$F_4$. We point out some issues concerning these two conventions and their
effect on tables about unipotent characters or the Springer correspondence.
Using experiments related to these issues with the computer algebra system {\sf
CHEVIE}, we spotted an error in Spaltenstein's tables for the generalised
Springer correspondence in type~$E_7$.

Representation Theory