I am looking at the vertex permutation representation of $D_4$ in $\mathbb R^4,$ where the vertices of the square are labelled $1,2,3,$ and $4.$ How do I prove that this representation has proper invariant subspaces?
2026-03-25 19:04:52.1774465492
Invariant Subspace of Vertex Representation of $D_4$
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The constant vectors form an invariant subspace.