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

2006/05/24 by James P. Cossey, Cossey, James P., Matthew Ondrus +3
Mathematics · #05E10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0605654

openalex publication_date 2006/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• The complexity of certain Specht modules for the symmetric group
• Specht Modules for Weyl Groups
• A new lower bound on the vertices of Specht modules for the symmetric groups
• Hoeffding spaces and Specht modules
• Vertices of Specht modules and blocks of the symmetric group