Decomposition numbers of exceptional Weyl groups. I (Q2266120)

The author computes the decomposition numbers of the exceptional Weyl groups for the prime \(p=3\). The technique used is similar to the one described by \textit{G. James} and \textit{A. Kerber} [The representation theory of the symmetric group. Reading, MA, etc.: Addison-Wesley (1981; Zbl 0491.20010), {\S} 6.3] for the symmetric groups, and involves inducing certain principal indecomposable characters of parabolic subgroups and separating the induced characters into p-blocks. When the parabolic subgroups are of classical type, the principal indecomposable characters are computed by a method given by \textit{J. Tappe} [Mitt. Math. Semin. Gießen 121, 39--57 (1976; Zbl 0361.20017)].