Linear maps preserving orbits
Representation Theory
2010-11-04 v5 Group Theory
Abstract
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.
Cite
@article{arxiv.0910.1308,
title = {Linear maps preserving orbits},
author = {Gerald W. Schwarz},
journal= {arXiv preprint arXiv:0910.1308},
year = {2010}
}
Comments
27 pages, minor changes. To appear in Annales de l'institut Fourier