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let $V$ be a complex representation of a finite group which is a direct sum of two nonismorphic irreducible representations $V_1$ and $V_2$. If $V_3$ is another representation isomorphic to $V_1$, how can I show $V_1=V_3$ as vector spaces. thank you

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  • $\begingroup$ What have you tried to do so far? $\endgroup$
    – YiFan Tey
    Commented Oct 27, 2019 at 5:02
  • $\begingroup$ @YiFan I can do it by projection,is that necessary? this statement appears as a direct result of Schur's lemma. $\endgroup$
    – ysTuan
    Commented Oct 27, 2019 at 5:19
  • $\begingroup$ It would be good if you can add your attempts to the question body with an edit, along with the context in which the problem occurs. People react quite negatively to homework-like questions, so you want to prevent misunderstanding. Cheers! $\endgroup$
    – YiFan Tey
    Commented Oct 27, 2019 at 5:23

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