When is the ring of invariants of a finite group generated by symplectic reflections a complete intersection ring? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T21:20:14Z http://mathoverflow.net/feeds/question/35993 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/35993/when-is-the-ring-of-invariants-of-a-finite-group-generated-by-symplectic-reflecti When is the ring of invariants of a finite group generated by symplectic reflections a complete intersection ring? zamanjan 2010-08-18T17:35:15Z 2010-08-18T17:35:15Z <p>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.</p> <p>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.</p>