TITLE: Is there a non-explicit characterization of the Specht modules?
QUESTION [9 upvotes]: 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.

REPLY [9 votes]: As Sam told me to do so, I convert my comment to an answer, although it is essentially the same as David Speyer's. 
The Specht module $S^\lambda$ is the unique simple module of $\mathfrak S_n$ whose restriction to the $\mathfrak S_\lambda$ contains the trivial and whose restriction to $\mathfrak S_{\lambda^*}$ contains the sign (where the star denotes conjugation of partitions, and with the usual notation for Young subgroups).
To see this, one just needs to know that if $S^\lambda$ occurs in the permutation module $M^\mu$, then $\lambda \geq \mu$ (for the dominance order), that tensoring with sign induces the transposition of partitions, and that the transposition is an anti-automorphism of the poset of partitions. The books by James, or James and Kerber, for example, can be used as a reference for those facts.