Minimal numbers of linear constituents in Sylow restrictions for symmetric groups

2025/05/23 by Gustavsson, Bim, Law, Stacey
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.17904

Abstract

Let p be any prime. We determine precisely those irreducible characters of symmetric groups which contain at most p distinct linear constituents in their restriction to a Sylow p-subgroup, answering a question of Giannelli and Navarro. Moreover, we identify all of the linear constituents of such characters, and in the case p = 2 explicitly calculate a new class of Sylow branching coefficients for symmetric groups indexed by so-called almost hook partitions.

Citations

• Sylow branching trees for symmetric groups
• Sylow branching coefficients and hook partitions
• Positivity of Sylow branching coefficients of symmetric groups
• On plethysms and Sylow branching coefficients
• Plethysms of symmetric functions and highest weight representations

Related

• Sylow branching coefficients and hook partitions
• Sylow branching trees for symmetric groups
• Linear characters of Sylow subgroups of symmetric groups
• A note on restriction of Characters of Alternating groups to Sylow\n Subgroups
• Sylow branching coefficients and a conjecture of Malle and Navarro