On the labelling of characters of Weyl groups of type \(F_4\)

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  \(F_4\) $F_4$ . 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 CHEVIE, we spotted an error in Spaltenstein’s tables for the generalised Springer correspondence in type  \(E_7\) $E_7$ .