Non-linear Sylow branching coefficients for symmetric groups

Abstract

We study the restriction to Sylow subgroups of irreducible characters of symmetric groups. In particular, we give a precise description of the degrees of the irreducible constituents in terms of the shape of the partition that labels a given irreducible character. Our main result is a wide generalization of [Giannelli and Navarro (Proc Am Math Soc 146(5):1963–1976, 2018), Theorem 3.1].