Hooks generate the representation ring of the symmetric group

2011/12/14 by Iván Marín, Marin, Ivan
Mathematics · #20C30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1112.3127

openalex publication_date 2011/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the representation ring of the symmetric group on n letters is generated by the exterior powers of its natural (n-1)-dimensional representation. The proof we give illustrates a strikingly simple formula due to Y. Dvir. We provide an application and investigate a possible generalization of this result to some other reflection groups.

Related

• Symmetric and Exterior Squares of Hook Representations
• Generators for the representation rings of certain wreath products
• Exterior powers of representations of finite groups and integer-valued characters
• A natural representation model for symmetric groups
• Irreducible decomposition and calculating of multiplicity of the symmetric and exterior powers representation of finite groups