On the local representation theory of symmetric groups

2025/06/05 by Greta Tendi, Tendi, Greta · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.04773

openalex publication_date 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a Sylow p-subgroup P of a symmetric group, we describe the action of its normalizer on Irr(P). To this end, we establish a one-to-one correspondence between the irreducible characters of P and certain equivalence classes of explicitly defined functions, which are also naturally suited to describing the Galois action.

Citations

• Sylow branching trees for symmetric groups

Cited by

• McKay bijections and character degrees

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• Linear characters of Sylow subgroups of symmetric groups
• Character correspondeces in solvable groups with a self-normalizing Sylow subgroup
• Irreducible Restrictions of Representations of Symmetric Groups in Small Characteristics: Reduction Theorems
• Irreducible restrictions of representations of symmetric and alternating groups in small characteristics
• A natural representation model for symmetric groups