rt.representation theory - Restriction from $GL_n$ to $S_n$

I keep meaning to post this and forgetting: Richard Stanley sent me the following two references

Enumerative Combinatorics, Volume II Exercise 7.74: If $V_{lambda}$ is a representation of $GL_n$, and $S_{mu}$ a representation of $S_n$, then the multiplicity of $S_{mu}$ in $mathrm{Restriction}^{GL_n}_{S_n} V_{lambda}$ is the coefficient of the Schur function $s_{lambda}$ in the symmetric formal power series
$$s_{mu}(1, x_1, x_2, ldots, x_1^2, x_1 x_2, x_1 x_3, ldots, x_1^3, x_1^2 x_2, ldots).$$
That is to say, we take the Schur function $s_{mu}$ and plug in every monomial. (Yes, for those who know the term, this is an example of plethysm.)

Gay, David A.
"Characters of the Weyl group of $SU(n)$ on zero weight spaces and centralizers of permutation representations."
Rocky Mountain J. Math. 6 (1976), no. 3, 449—455.

Determines the representation of $S_n$ on the zero weight space of $V_{lambda}$ when $|lambda|$ is a multiple of $n$.

I just found another reference, which I haven't digested yet: Scharf, Thibon and Wybourne (1997).