Constructing all irreducible Specht modules in a block of the symmetric group

Cossey, James P.; Ondrus, Matthew; Vinroot, C. Ryan

Constructing all irreducible Specht modules in a block of the symmetric group

Authors

Cossey, James P.

Ondrus, Matthew

Vinroot, C. Ryan

Description

For 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.