Decomposition numbers of exceptional Weyl groups. II
[For Part I, cf. the first author, ibid. 91, 390-409 (1984; Zbl 0559.20011).] In this work, the modular irreducible characters of the exceptional Weyl groups for the prime numbers \(p=5,7\) are determined. The only groups which need to be considered are those of type E, namely, \(W(E_ 6)\), \(W(E_ 7)\) and \(W(E_ 8)\). In all cases but one, namely, \(W(E_ 8)\) and \(p=5\), the relevant prime number divides the order of the group to the first power only.
scientific article; zbMATH DE number 4071182