Let $G<\rm{GL}_n(\mathbb{k})$ be a linear group, where $\mathbb{k}$ is an algebraically closed field. Assume that the linear action of $G$ on $\mathbb{k}^n$ is strongly-irreducible (i.e. there are no $H$-invariant proper subspaces of $\mathbb{k}^n$, except $0$, for any $H Thanks for any help.
Existence of proper invariant subset in an irreducible action
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linear-algebra
1 Answers
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Maybe I missed something here, but isn't $U=\mathbb{k}^n-0$ a candidate?
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0Yeah, well, it's clearly an example, but could there be such a $U$ when it's compliment is not $0$? – 2011-04-29