It is a basic fact about the symmetric group $S_n$ that its irreducible representations are indexed by partitions of $n$.

My question is, can the association between partitions and irreps be specified without having to explicitly construct the irreps? In other words, is there for each partition $\lambda$ some relatively simple property that is possessed by the Specht module $S^\lambda$ but none of the other irreps of $S_n$?

In particular I was imagining that an answer might come from Jucys-Murphy type theory but I am not familiar enough with the material to know how to (or if it is possible to) use it to characterize $S^\lambda$ without having to give a bunch of background information.

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