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  "body": "\n## Summary\n\nThe representation theory of the [[symmetric group|0515A6D2Y1]] $S_n$ studies its [[representations|WYGRXCG2RN]] and characters.\nOver the complex numbers, the irreducible representations of $S_n$ correspond to the [[partitions|0JV30XN73Z]] of $n$, and are realised by the [[Specht modules|NTFM7X5555]].\nThe theory is fully combinatorial: [[Young diagrams|096AHMB3P4]] and [[Young tableaux|Q6TH9PH2R7]] give dimensions and characters.\nIt connects with symmetric functions, the representations of general linear groups and many parts of combinatorics and physics.\n\n## Explanations\n\n### L1 human\n\nThe symmetric group consists of all shufflings of $n$ objects.\nIts irreducible representations are labelled by the ways of writing $n$ as a sum of positive integers, drawn as left-justified rows of boxes.\nFor $n = 3$ there are three partitions, $3$, $2 + 1$ and $1 + 1 + 1$, matching the trivial, the two-dimensional and the sign representations of $S_3$.\nThe dimension of each one is the number of ways to fill its diagram with $1, \\ldots, n$ increasing along rows and down columns.\n",
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