Regions in the dominant chamber and nilpotent orbits

AbstractLet G be a complex semisimple algebraic group with Lie algebra g. The goal of this note is to show that combining some ideas of Gunnells and Sommers [Math. Res. Lett. 10 (2–3) (2003) 363–373] and Vinberg and Popov [Invariant Theory, in: Algebraic Geometry IV, in: Encyclopaedia Math. Sci., Vol. 55, Springer, Berlin, 1994, pp.123–284] yields a geometric description of the characteristic of a nilpotent G-orbit in an arbitrary (finite-dimensional) rational G-module