  Tevelev has given a remarkable explicit formula for the discriminant of a
complex simple Lie algebra, which can be defined as the equation of the dual
hypersurface of the minimal nilpotent orbit, or of the so-called adjoint
variety. In this paper we extend this formula to the setting of graded Lie
algebras, and express the equation of the corresponding dual hypersurfaces in
terms of the reflections in the little Weyl groups, the associated complex
reflection groups. This explains for example why the codegree of the
Grassmannian $G(4, 8)$ is equal to the number of roots of $\mathfrak{e}_7$ .
