Irreducibility of G-varieties defined by quadrics
  Let $\mathfrak{g}$ be a complex semisimple Lie algebra, $G$ a simply connected and connected Lie group with Lie algebra $\mathfrak{g}$ and $V$ a finite dimensional representation. We prove that the zero locus of quadrics containing $G.y$ is an irreducible variety in $\PP V$. 
Cesar Massri
math.AG