Linear maps preserving orbits
Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 667-706.

Let HGL(V) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let vV and let G={g GL (V)gHv=Hv}. Following Raïs we say that the orbit Hv is characteristic for H if the identity component of G is H. If H is semisimple, we say that Hv is semi-characteristic for H if the identity component of G is an extension of H by a torus. We classify the H-orbits which are not (semi)-characteristic in many cases.

Soit HGL(V) un groupe complexe réductif connexe où V est un espace vectoriel complexe de dimension finie. Soient vV et G={g GL (V)gHv=Hv}. D’aprés Raïs nous disons que l’orbite Hv est caractéristique pour H si la composante connexe de l’identité de G est H. Si H est semi-simple, nous disons que Hv est semi-caractéristique pour H si la composante connexe de l’identité de G est une extension de H par un tore. Nous classifions les orbites de H qui ne sont pas (semi)-caractéristiques dans plusieurs cas.

DOI: 10.5802/aif.2691
Classification: 20G20, 22E46
Keywords: Characteristic orbits, linear preserver problems
Mot clés : Orbites caractéristiques, problèmes de préservation linéaires
Schwarz, Gerald W. 1

1 Brandeis University Department of Mathematics Waltham, MA 02454-9110 (USA)
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Schwarz, Gerald W. Linear maps preserving orbits. Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 667-706. doi : 10.5802/aif.2691. http://www.numdam.org/articles/10.5802/aif.2691/

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