Representations of monomial matrices and restriction from $G{L}_n$ to $S_n$

We outline an approach to understanding restrictions of polynomial representations of $G{L}_n(\mathbb{C})$ to $S_n$ by first restricting to $T \rtimes S_n$,thesubgroupof$n \times n$ monomial matrices. Using this approach we give a combinatorial interpretation for the decomposition of a tensor product of symmetric powers of the defining representation.