On plethysms and Sylow branching coefficients

2021/10/27 by Stacey Law, Law, Stacey, Yuji Okitani +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2110.14552

openalex publication_date 2021/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a recursive formula for plethysm coefficients of the form a^μ_λ,(m), generalising results on plethysms due to Bruns--Conca--Varbaro and de Boeck--Paget--Wildon. From this we deduce a stability result and resolve two conjectures of de Boeck concerning plethysms, as well as obtain new results on Sylow branching coefficients for symmetric groups for the prime 2. Further, letting P_n denote a Sylow 2-subgroup of S_n, we show that almost all Sylow branching coefficients of S_n corresponding to the trivial character of P_n are positive.

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• Minimal numbers of linear constituents in Sylow restrictions for symmetric groups

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