Dimensions of the Irreducible Representations of the Symmetric and Alternating Group

  • Korneel Debaene
DOI: https://doi.org/10.37236/4909
Keywords: Representations, Symmetric group, Alternating group, Hook Formula, Primes in short intervals

Abstract

We establish the existence of an irreducible representation of $A_n$ whose dimension does not occur as the dimension of an irreducible representation of $S_n$, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals. 

Published
2016-09-30
Issue
Volume 23, Issue 3 (2016)
Article Number
P3.49