Is the Luna stratification intrinsic?

Jochen Kuttler[1]; Zinovy Reichstein[2]

  • [1] University of British Columbia Department of Mathematics Vancouver, BC V6T 1Z2 (Canada) Current address: University of Alberta Department of Mathematical and Statistical Sciences Edmonton, AB T6G 2G1 (Canada)
  • [2] University of British Columbia Department of Mathematics Vancouver, BC V6T 1Z2 (Canada)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 2, page 689-721
  • ISSN: 0373-0956

Abstract

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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, 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.

How to cite

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Kuttler, Jochen, and Reichstein, Zinovy. "Is the Luna stratification intrinsic?." Annales de l’institut Fourier 58.2 (2008): 689-721. <http://eudml.org/doc/10329>.

@article{Kuttler2008,
abstract = {Let $G \rightarrow \operatorname\{GL\}(V)$ 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 $X = V \mathmo\{//\}G$ 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 $V \mathmo\{//\}G$ map each stratum to another stratum?(ii) Are the individual Luna strata in $X$ intrinsic? That is, does every automorphism of $V \mathmo\{//\}G$ 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.},
affiliation = {University of British Columbia Department of Mathematics Vancouver, BC V6T 1Z2 (Canada) Current address: University of Alberta Department of Mathematical and Statistical Sciences Edmonton, AB T6G 2G1 (Canada); University of British Columbia Department of Mathematics Vancouver, BC V6T 1Z2 (Canada)},
author = {Kuttler, Jochen, Reichstein, Zinovy},
journal = {Annales de l’institut Fourier},
keywords = {Categorical quotient; Luna stratification; matrix invariant; representation type; categorical quotient},
language = {eng},
number = {2},
pages = {689-721},
publisher = {Association des Annales de l’institut Fourier},
title = {Is the Luna stratification intrinsic?},
url = {http://eudml.org/doc/10329},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Kuttler, Jochen
AU - Reichstein, Zinovy
TI - Is the Luna stratification intrinsic?
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 2
SP - 689
EP - 721
AB - Let $G \rightarrow \operatorname{GL}(V)$ 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 $X = V \mathmo{//}G$ 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 $V \mathmo{//}G$ map each stratum to another stratum?(ii) Are the individual Luna strata in $X$ intrinsic? That is, does every automorphism of $V \mathmo{//}G$ 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.
LA - eng
KW - Categorical quotient; Luna stratification; matrix invariant; representation type; categorical quotient
UR - http://eudml.org/doc/10329
ER -

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