The largest character degrees of the symmetric and alternating groups

Zoltán Halasi, Carolin Hannusch, Hung Ngoc Nguyen

We show that the largest character degree of an alternating group $A_n$ with $n\ge 5$ can be bounded in terms of smaller degrees in the sense that \[ b(A_n)^2<\sum_{ψ\in\textrm{Ir…