Let be a connected complex reductive group where is a finite-dimensional complex vector space. Let and let . Following Raïs we say that the orbit is characteristic for if the identity component of is . If is semisimple, we say that is semi-characteristic for if the identity component of is an extension of by a torus. We classify the -orbits which are not (semi)-characteristic in many cases.
Soit un groupe complexe réductif connexe où est un espace vectoriel complexe de dimension finie. Soient et . D’aprés Raïs nous disons que l’orbite est caractéristique pour si la composante connexe de l’identité de est . Si est semi-simple, nous disons que est semi-caractéristique pour si la composante connexe de l’identité de est une extension de par un tore. Nous classifions les orbites de qui ne sont pas (semi)-caractéristiques dans plusieurs cas.
Keywords: Characteristic orbits, linear preserver problems
Mot clés : Orbites caractéristiques, problèmes de préservation linéaires
Schwarz, Gerald W. 1
@article{AIF_2012__62_2_667_0, author = {Schwarz, Gerald W.}, title = {Linear maps preserving orbits}, journal = {Annales de l'Institut Fourier}, pages = {667--706}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {2}, year = {2012}, doi = {10.5802/aif.2691}, mrnumber = {2985513}, zbl = {1255.14040}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2691/} }
TY - JOUR AU - Schwarz, Gerald W. TI - Linear maps preserving orbits JO - Annales de l'Institut Fourier PY - 2012 SP - 667 EP - 706 VL - 62 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2691/ DO - 10.5802/aif.2691 LA - en ID - AIF_2012__62_2_667_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.2691/
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