I am trying to solve a question, but I do not know what the notation used means. If anyone could help me out that'd be great! I don't need help doing the proof, just what the notation means would be brilliant.

I have a finite group $G$ and $V, W$ finite-dimensional $\mathbb{C}G$-modules. Let $L:V\rightarrow W$ be a linear map and define $p:V\rightarrow W$ by $p(x)=\sum\_{g\in G}g^{-1}Lg(x)$.

Prove that $p$ is a homomorphism of $\mathbb{C}G$-modules.

I don't understand the what the definition of $p$ means.

Thanks,

Andy.