Linear maps preserving orbits

Details Linear maps preserving orbits Linear maps preserving orbits

2009-10-07

arxiv.org/abs/0910.1308v5

Mathematics

Representation Theory

27 pages, minor changes. To appear in Annales de l'institut Fourier

Scientific paper

Let H\subset\GL(V) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v\in V and let G=\{g\in\GL(V)\mid gHv = Hv\}. Following Ra\"is we say that the orbit Hv is \emph{characteristic for H} if the identity component of G is H. If H is semisimple, we say that Hv is \emph{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.

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