Sylow branching trees for symmetric groups

Eugenio Giannelli; Stacey Law

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Sylow branching trees for symmetric groups

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arxiv 2409.07575 v2 pith:64OIYBMF submitted 2024-09-11 math.RT math.COmath.GR

Sylow branching trees for symmetric groups

Eugenio Giannelli , Stacey Law This is my paper

classification math.RT math.COmath.GR

keywords sylowsymmetrictreesbranchingcharactersgroupsirreduciblearticle

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

Sylow branching trees for symmetric groups

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