Consider $V$, V_{(n-1, 1)}$, the $n-1$ dimensional irreducible representation of $S_n$, i.e. the "standard" or "defining" representation. Is there a nice formula for how the $k$-th tensor power of $V$ V_{(n-1, 1)}$ decomposes into irreps?
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Tensor powers of the standard representationConsider $V$, the $n-1$ dimensional irreducible representation of $S_n$, i.e. the "standard" or "defining" representation. Is there a nice formula for how the $k$-th tensor power of $V$ decomposes into irreps?
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