On the restriction of a character of \(\mathfrak{S}_n\) to a Sylow \(p\)-subgroup

Abstract: The relevance of the McKay Conjecture in the representation theory of finite groups has led to investigate how irreducible characters decompose when restricted to Sylow \(p\)-subgroups. In this talk we will focus on the symmetric groups. Since the linear constituents of the restriction to a Sylow \(p\)-subgroup has been studied a lot by E. Giannelli and S. Law, we will concentrate on constituents of higher degree. In particular, we will describe the set of the irreducible characters which allow a constituent of a fixed degree, separating the cases of \(p\) being odd and \(p=2\). This is a joint work with Eugenio Giannelli.

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.