Some Properties of Generalized Foulkes Module

2021/10/03 by Pál Hegedüs, Hegedüs, Pál, Sai Praveen Madireddi +1
Mathematics · #Advanced Mathematical Identities #Analytic and geometric function theory #FOS: Mathematics #Mathematical functions and polynomials #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2110.01055

openalex publication_date 2021/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Describing the decomposition of Foulkes module F_b^a into irreducible Specht modules is an open problem for a,b > 3. In this article we provide a new approach for the Generalized Foulkes module F_ν^a (with arbitrary partition ν of b) through its restriction to a maximal Young subgroup S_b × S_{ab -b}.

Related

• On the decomposition of the Foulkes module
• Constructing all irreducible Specht modules in a block of the symmetric group
• Indecomposable summands of Foulkes modules
• Irreducible Specht modules are signed Young modules
• Young's seminormal form and simple modules for S_n in characteristic p