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Is the Luna stratification intrinsic?

Jochen Kuttler;  Zinovy Reichstein — 2008

Annales de l’institut Fourier

Let G → GL ( V ) be a representation of a reductive linear algebraic group G on a finite-dimensional vector space V , defined over an algebraically closed field of characteristic zero. The categorical quotient X = V // G carries a natural stratification, due to D. Luna. This paper addresses the following questions: (i) Is the Luna stratification of X intrinsic? That is, does every automorphism of V // G map each stratum to another stratum? (ii) Are the individual Luna strata in X intrinsic? That is,...

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