I am trying to understand first how one can define the plethysm say $s_\lambda \circ s_\mu$ as a module in the regular representation of the symmetric group.
1)How is it connected to the plethysms in Schur functions.
2)Do the multiplicities of the irreducible decomposition and the corresponding schur expansion match? (reference?)
Is there a simple way to understand the plethysm in regular representation of $S_n$. I tried to read around and found that involves 'wreath products' I don't fully understand this, as my background is in physics.
3)Can any one explain in 'simple terms' using perhaps a simple example $s_2 \circ s_2$ (as representation of $S_4$)?