Sylow branching coefficients and a conjecture of Malle and Navarro

Stacey Law (University of Cambridge)

13-Apr-2021, 07:30-08:30 (3 years ago)

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.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic


OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.

Organizer: Liron Speyer*
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