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  "body": "\n## Summary\n\nFor each [[partition|0JV30XN73Z]] $\\lambda$ of $n$, the Specht module $S^\\lambda$ is a representation of the [[symmetric group|0515A6D2Y1]] $S_n$ built from [[Young tableaux|Q6TH9PH2R7]] of shape $\\lambda$.\nOver a field of characteristic $0$, the Specht modules are irreducible and give every irreducible representation of $S_n$ exactly once.\nThey are defined over any field, even over the integers.\nThe dimension of $S^\\lambda$ is the number of standard Young tableaux of shape $\\lambda$, given by the [[hook length formula|VCMS1CP91N]].\n\n## Explanations\n\n### L1 human\n\nA Specht module turns a picture, a [[Young diagram|096AHMB3P4]], into a representation of the symmetric group.\nOne fills the diagram with the numbers $1$ to $n$ and forms a signed sum that is symmetric along rows and antisymmetric down columns.\nThe span of all such sums is the module.\nA single row gives the trivial representation, and a single column gives the sign representation.\n",
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