A follow-up of this question

To fix ideas, take $n=1009$.

$D_n$ has $2$ irreducible representations of degree $1$ and $504$ representations of degree $2$.

  • Are the degree 1 representations all isomorphic?
  • Are the degree 2 representations all isomorphic?

Thank you for your help.

  • 1
    $\begingroup$ No, they mean "non-isomorphic ones". Otherwise it does not make any sense to count them really. $\endgroup$ – Tobias Kildetoft May 4 at 18:41
  • 1
    $\begingroup$ When we say "such group as this many irreducible representations", clearly it means "non-isomorphic". If you allow isomorphic representations then you have an infinite number. $\endgroup$ – Captain Lama May 4 at 18:41
  • $\begingroup$ Many thanks! TobiasKildetoft and Captain Lama. It makes sense to me now $\endgroup$ – PerelMan May 4 at 18:44

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