I am given $\lambda$ a partition of n and I am asked to show that $\mathcal{F}(1_{triv,\lambda}\uparrow_{S_\lambda}^{S_n}) = h_\lambda$ where $\mathcal{F}$ is the Frobenius character. I don't really know how to use any of the definitions to solve this problem.
$h_\lambda$ are the homogeneous basis for the symmetric functions.