On the $p^{\prime }$-subgraph of the Young graph

Abstract

Let $p$ be a prime number. In this article we study the restriction to ${\mathfrak{S}}_{n-1}$ of irreducible characters of degree coprime to $p$ of ${\mathfrak{S}}_n$. In particular, we study the combinatorial properties of the subgraph ${\mathbb{Y}}_{p^{\prime }}$ of the Young graph $\mathbb{Y}$. This is an extension to odd primes of the work done by Ayyer, Prasad and Spallone for $p=2$.

21 pages