Let $s_\lambda \circ s_\mu$ be a plethysm. Here let $\lambda, \mu$ be $m,n$ box Young diagrams.
I have seen the definition of plethysms in symmetric functions. I would like to understand the corresponding realisation of plethysms as the regular representations of the permutation group, in this case $S_{mn}$.
If possible can you please explain this in a way a physicist can understand?