Geodesic
On same-invariant linear groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 134-148

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A linear group $G\le GL(V)$ is called same-invariant if the subspaces of linear invariants $V^g$ are the same for all $g\in G, g\ne1$. Below we consider properities of such a group $G$ under the assumption that $G$ contains unipotent elements. 
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     title = {On same-invariant linear groups},
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N. L. Gordeev; N. F. Kushpel'. On same-invariant linear groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 134-148. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a7/