Vector Fields and Luna Strata

Details Vector Fields and Luna Strata Vector Fields and Luna Strata

2011-10-16

arxiv.org/abs/1110.3523v2

Mathematics

Group Theory

7 pages, minor changes, to appear in Communications in Pure and Applied Algebra

Scientific paper

Let 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 phi : Z\to Z is any automorphism, does phi send strata to strata? In a paper of Kuttler and Reichstein 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.

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