Let $S_{n-1}$ be the subgroup of $S_n$ that fixes n. Consider sgn to be the permutation sign representation of $S_{n-1}$ as a $\mathbb C$-representation.
What is the decomposition of the induced representation of sgn to $S_n$?
I know by Frobenius reciprocity that $sgn_{S_n}$ appears once. My guess is that $standard_{S_n}$ appears once.
I have looked at another question on this site that does it for $S_3$ and $S_2$. How to do it in general?