Sylow branching trees for symmetric groups

Eugenio Giannelli; Stacey Law

doi:10.1090/tran/9469

Sylow branching trees for symmetric groups

Eugenio Giannelli
, Stacey Law

Mathematics

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Abstract

Let p ≥ 5 be a prime and let P be a Sylow p-subgroup of a finite symmetric group S_n. To every irreducible character of P we associate a collection of labelled, complete p-ary trees. The main results of this article describe the positivity of Sylow branching coefficients for all irreducible characters of P in terms of combinatorial properties of these trees, extending previous work on the linear characters of P.

Original language	English
Journal	Transactions of the American Mathematical Society
Early online date	16 Jul 2025
DOIs	https://doi.org/10.1090/tran/9469
Publication status	E-pub ahead of print - 16 Jul 2025

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abstract = "Let p ≥ 5 be a prime and let P be a Sylow p-subgroup of a finite symmetric group Sn. To every irreducible character of P we associate a collection of labelled, complete p-ary trees. The main results of this article describe the positivity of Sylow branching coefficients for all irreducible characters of P in terms of combinatorial properties of these trees, extending previous work on the linear characters of P. ",

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AB - Let p ≥ 5 be a prime and let P be a Sylow p-subgroup of a finite symmetric group Sn. To every irreducible character of P we associate a collection of labelled, complete p-ary trees. The main results of this article describe the positivity of Sylow branching coefficients for all irreducible characters of P in terms of combinatorial properties of these trees, extending previous work on the linear characters of P.

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JO - Transactions of the American Mathematical Society

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Sylow branching trees for symmetric groups

Abstract

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