For all n > 2, how does one decompose the defining permutation representation of the symmetric group $S_n$ into irreducible representations?
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Depends. Does one start with knowledge of all the irreducible representations? Then, it's easy. If not, then, it's hard, and gets harder the larger $n$ is. – Gerry Myerson Feb 13 '20 at 04:13
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@Gerry I would understand "defining permutation representation" as the degree $n$ one, in which case the answer is essentially the same in all cases (in char 0). – Tobias Kildetoft Feb 13 '20 at 08:20