Stability of Restrictions of Representations of the Symmetric Group to the Hyperoctahedral Subgroup

2025/04/13 by Sergey N. Davydov, Davydov, Sergey
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2504.09560

openalex publication_date 2025/04/13 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

The paper investigates the stability properties of restrictions of irreducible representations of the symmetric group to the hyperoctahedral subgroup. A stability result is obtained, analogous to the classical Murnaghan theorem on the stability of the decomposition of tensor products of representations of the symmetric group. The proof is based on the description of these restrictions in terms of symmetric functions from the K. Koike and I. Terada's paper.

Related

• The classification of the stable factor-representations of the infinite hyperoctahedral group
• Irreducible restrictions of representations of symmetric and alternating\n groups in small characteristics
• Irreducible Restrictions of Representations of Symmetric Groups in Small\n Characteristics: Reduction Theorems
• Branching rules for the Weyl Groups of the Unitary and Orthogonal Lie Groups
• On the decomposition of tensor representations of symmetric groups