A GIT characterization of cofree representations

Let $V$ be a representation of a connected reductive group $G$. A representation is cofree if $k[V]$ is a free $k[V]^G$ module. There is a long history of work studying and classifying cofree representations of reductive groups. In this talk I present a simple conjectural characterization of cofree representations in terms of geometric invariant theory. Matt Satriano and I have proved the conjecture for irreducible representations of SL_n as well as for torus actions. I will give motiviation for the conjecture and explain the techniques which can be used for its verification. This talk based on joint work with Matt Satriano.