Dimensions of the Irreducible Representations of the Symmetric and Alternating Group

Korneel Debaene

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. 


Keywords


Representations, Symmetric group, Alternating group, Hook Formula, Primes in short intervals

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