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?
Consider $V$, 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?