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  "body": "\n## Summary\n\nGiven a field extension $K/F$, a representation *V* of a group *G* over *K* is said to be defined over *F* if $V \\simeq V_0 \\otimes_F K$ for some representation $V_0$ over *F* such that $g: V \\to V$ is induced by $g: V_0 \\to V_0$; i.e., $g \\cdot (v \\otimes \\lambda) = g v \\otimes \\lambda$. Here, $V_0$ is called an *F*-form of *V* (and is not necessarily unique).\n",
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