Sylow branching trees for symmetric groups

Source abstract

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