Decomposition numbers for symmetric groups and composition factors of Weyl modules
Let \(K\) be an algebraically closed field of prime characteristic \(p\) and \(n \in N\). The author proves that the composition multiplicities of Weyl modules for \(\text{GL} (n,k)\) are equal to decomposition numbers of the symmetric group \(S_r\) when \(r\) is allowed to vary. This result is a generalization of a result obtained by \textit{G. D. James} [Math. Z. 172, 161-178 (1980; Zbl 0438.20008)] where it is proved in the case of \(r = n\).
composition multiplicities of Weyl modules
scientific article; zbMATH DE number 869815
scientific article