Equivariant differential forms.

Question

I have some question about the equivariant differential forms on a smooth manifold: \ The equivariant differential forms over some smooth manifold $M$, on which the compact Lie group $G$ acts, are defined to be $$ \Omega_{G}^q(M)= \oplus_{2i+j=q} (S^{i}(\mathfrak g^*) \otimes \Omega^j(M))^G, $$ where $\mathfrak g^*$ denotes the dual of the Lie algebra $\mathfrak g$ of $G$. Then many authors say that these forms can be considered as polynomial functions on the Lie algebra $\mathfrak g$ of $G$, but I am not sure how this is to be done. For example if we consider the element $(x_1 \otimes... \otimes x_i) \otimes \omega$ where $x_1,..., x_i$ are elements of $\mathfrak g^*$ and $\omega$ is a differential form, what is the evaluation of this element on some $a \in \mathfrak g$ in the Lie algebra of $G$.