Let V be a finite dimensional symplectic vector space over $\mathbb{C}$. Let $G$ be a finite subgroup of the symplectic group $Sp(V),$ which is generated by symplectic reflections, i.e. by elements $g\in G,$ such that $rank(Id_V-g)=2.$ Then it is well-known that the ring of invariants $\mathbb{C}[V]^G$ is Gorenstein.
My question is assuming that V is an irreducible G-module and $dim V>2,$ when is $\mathbb{C}[V]^G$ a complete intersection ring? Of course when $dim V=2$ it is a complete intersection ring (Kleinian singularities), but I don't know other examples.
