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 joint work with Eugenio Giannelli.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
