a b s t r a c tLet V be a G-module, where G is a complex reductive group. Let Z := V / /G denote the categorical quotient. One can ask if the Luna stratification of Z is intrinsic. That is, if ϕ : Z → Z is any automorphism, does ϕ send strata to strata? In Kuttler and Reichstein (2008) [1], the answer was shown to be yes for V a direct sum of sufficiently many copies of a G-module W . We show that the answer is yes for almost all V . The key is to consider the vector fields on Z . Our methods also show that complex analytic automorphisms preserve the stratification.