Is the Luna stratification intrinsic?

J. Kuttler; Z. Reichstein

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arXiv · math/0610669

Is the Luna stratification intrinsic?

J. Kuttler·Z. Reichstein

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Abstract

Let G -> \GL(V) be a finite-dimensional linear 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 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, does every automorphism of V//G maps each stratum to itself? In general, the Luna stratification is not intrinsic. Nevertheless, we give positive answers to questions (i) and (ii) for large classes of interesting representations.

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J. Kuttler, Z. Reichstein. 2006-10-23. Is the Luna stratification intrinsic?. https://arxiv.org/abs/math/0610669

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