OIST Representation Theory Seminar

Speaker: Stacey Law, University of Cambridge

Title: Sylow branching coefficients and a conjecture of Malle and Navarro

Abstract: The relationship between the representation theory of a finite group and that of its Sylow subgroups is a key area of interest. For example, recent results of Malle–Navarro and Navarro–Tiep–Vallejo have shown that important structural properties of a finite group \(G\) are controlled by the permutation character \(\mathbb{1}_P\big\uparrow^G\), where \(P\) is a Sylow subgroup of \(G\) and \(\mathbb{1}_P\) denotes the trivial character of \(P\). We introduce so-called Sylow branching coefficients for symmetric groups to describe multiplicities associated with these induced characters, and as an application confirm a prediction of Malle and Navarro from 2012, in joint work with E. Giannelli, J. Long and C. Vallejo.

Zoom info can be found on the seminar webpage.