2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112903For any prime p, we construct, and simultaneously count, all of the complex Specht modules in a given p-block of the symmetric group which remain irreducible when reduced modulo p. We call the Specht modules with this property p-irreducible modules. Recently Fayers has proven a conjecture of James and Mathas that provides a characterization of the partitions that correspond to the p-irreducible modules. In this paper we present a method for decomposing the partitions corresponding to p-irreducible modules, and we use this decomposition to construct and count all of the partitions corresponding to p-irreducible Specht modules in a given block.CombinatoricsRepresentation Theory05E10text