2009/10/07 by Gerald W. Schwarz, Schwarz, Gerald W.
Mathematics · #20G20 #22E46 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20G20 #msc:22E46
paper · pdf · doi:10.48550/arxiv.0910.1308
27 pages, minor changes. To appear in Annales de l'institut Fourier
arxiv created 2010/11/03 · arxiv updated 2010/11/04
Let H⊂\GL(V) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v∈ V 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.