ar X iv : m at h / 06 10 66 9 v 1 [ m at h . A G ] 2 3 O ct 2 00 6 IS THE LUNA STRATIFICATION INTRINSIC ?
نویسندگان
چکیده
Let G → GL(V) will 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 automor-phism 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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