Let be a representation of a reductive linear algebraic group on a finite-dimensional vector space , defined over an algebraically closed field of characteristic zero. The categorical quotient carries a natural stratification, due to D. Luna. This paper addresses the following questions:
(i) Is the Luna stratification of intrinsic? That is, does every automorphism of map each stratum to another stratum?
(ii) Are the individual Luna strata in intrinsic? That is, does every automorphism of 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.
Soit une représentation d’un groupe algébrique réductif , définie sur un corps algébraiquement clos de caractéristique zéro. D’après D. Luna, le quotient catégorique comporte une stratification naturelle. L’article présente les deux questions suivantes :
(i) La stratification de est-elle intrinsèque ? Plus précisément, l’image d’une strate par un automorphisme de quelconque est-elle avec strate ?
(ii) Les strates individuelles de , sont-elles intrinsèques ? C’est-à-dire, est-il vrai que toute strate est invariante par tous les automorphismes de ?
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.
Keywords: Categorical quotient, Luna stratification, matrix invariant, representation type
Mot clés : quotient catégorique, stratification de Luna, invariants de matrices, type de representation
Kuttler, Jochen 1; Reichstein, Zinovy 2
@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}, pages = {689--721}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2365}, mrnumber = {2410387}, zbl = {1145.14047}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2365/} }
TY - JOUR AU - Kuttler, Jochen AU - Reichstein, Zinovy TI - Is the Luna stratification intrinsic? JO - Annales de l'Institut Fourier PY - 2008 SP - 689 EP - 721 VL - 58 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2365/ DO - 10.5802/aif.2365 LA - en ID - AIF_2008__58_2_689_0 ER -
%0 Journal Article %A Kuttler, Jochen %A Reichstein, Zinovy %T Is the Luna stratification intrinsic? %J Annales de l'Institut Fourier %D 2008 %P 689-721 %V 58 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2365/ %R 10.5802/aif.2365 %G en %F AIF_2008__58_2_689_0
Kuttler, Jochen; Reichstein, Zinovy. Is the Luna stratification intrinsic?. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 689-721. doi : 10.5802/aif.2365. https://aif.centre-mersenne.org/articles/10.5802/aif.2365/
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