Symmetric and Exterior Squares of Hook Representations

2019/09/16 by Szabolcs Mészáros, Mészáros, Szabolcs, János Wolosz +1
Mathematics · #05E10 #20B30 #20C30 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1909.07489

openalex publication_date 2019/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the multiplicities of irreducible summands in the symmetric and the exterior squares of hook representations of symmetric groups over an algebraically closed field of characteristic zero.

Related

• Hooks generate the representation ring of the symmetric group
• Irreducible decomposition and calculating of multiplicity of the symmetric and exterior powers representation of finite groups
• The Howe duality and the Projective Representations of Symmetric Groups
• Hook Theorem for Superalgebras with Superinvolution or Graded Involution
• Surprising Relations Between Sums-Of-Squares of Characters of the Symmetric Group Over Two-Rowed Shapes and Over Hook Shapes