Is the Luna stratification intrinsic?  [ La stratification de Luna, est-elle intrinsèque ? ]
Annales de l'Institut Fourier, Tome 58 (2008) no. 2, p. 689-721
Soit GGL(V) une représentation d’un groupe algébrique réductif G, définie sur un corps algébraiquement clos de caractéristique zéro. D’après D. Luna, le quotient catégorique X=V//G comporte une stratification naturelle. L’article présente les deux questions suivantes :(i) La stratification de X est-elle intrinsèque ? Plus précisément, l’image d’une strate par un automorphisme de X quelconque est-elle avec strate ?(ii) Les strates individuelles de X, sont-elles intrinsèques ? C’est-à-dire, est-il vrai que toute strate est invariante par tous les automorphismes de X ?D’une manière générale, la stratification de Luna n’est pas intrinsèque. Néanmoins, pour des familles de représentations intéressantes les questions (i) et (ii) ont des réponses positives.
Let GGL(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, does every automorphism of V//G map each stratum to itself?In general, the Luna stratification is not intrinsic. Nevertheless, we give positive answers to questions (i) and (ii) for interesting families of representations.
DOI : https://doi.org/10.5802/aif.2365
Classification:  14R20,  14L30,  14B05
Mots clés: quotient catégorique, stratification de Luna, invariants de matrices, type de representation
@article{AIF_2008__58_2_689_0,
     author = {Kuttler, Jochen and Reichstein, Zinovy},
     title = {Is the Luna stratification intrinsic?},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {2},
     year = {2008},
     pages = {689-721},
     doi = {10.5802/aif.2365},
     mrnumber = {2410387},
     zbl = {1145.14047},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2008__58_2_689_0}
}
Kuttler, Jochen; Reichstein, Zinovy. Is the Luna stratification intrinsic?. Annales de l'Institut Fourier, Tome 58 (2008) no. 2, pp. 689-721. doi : 10.5802/aif.2365. http://www.numdam.org/item/AIF_2008__58_2_689_0/

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