OIST Representation Theory Seminar

Bim Gustavsson, University of Birmingham

Title: Sylow branching coefficients and counting linear constituents

Abstract: For a natural number \(n\), let \(P_n\) denote a Sylow \(p\)-subgroup of the symmetric group \(S_n\). In 2017 E. Giannelli and G. Navarro proved that if \(\chi\) is an irreducible character of \(S_n\) with degree divisible by \(p\), then the restriction of \(\chi\) to \(P_n\) has at least \(p\) different linear constituents. In this talk we will present the result that classifies the set of irreducible characters of the symmetric groups whose restriction to \(P_n\) have at most \(p\) linear constituents when \(p=2\). We will also for mention the multiplicity of these linear characters for certain families of irreducible characters of \(S_n\).

Zoom info can be found on the seminar webpage.