# Why are rational functions invariant under symmetric linear group generated by Plucker coordinates

I am working on an exercise and not sure where to start.

Let $$K=(\mathbb{C}^2)^{n+3}$$. The special linear group $$SL_2$$ acts naturally on each $$\mathbb{C}^2$$ and hence on $$K$$. Let $$R$$ be the field of rational functions on $$K$$. The claim is that the subfield $$F$$ of $$K$$ which is invariant under the action of $$SL_2$$ is generated by the Plucker coordinates $$\det(v_i,v_j)$$, where each $$v_i\in\mathbb{C}^2$$.

It is clear to me that each Plucker coordinate is in fact $$SL_2$$ invariant, but I am unclear on how to prove that $$F$$ is actually generated by these coordinates.

Thanks!