Corollary

Tag 03DP, permanent. Cite it as [Bourbaki, Tag 03DP].

Théories spectrales, chapter V, § 4. Représentations des groupes compacts

Let $\varrho_1$ and $\varrho_2$ be finite-dimensional representations of G. The representations $\varrho_1$ and $\varrho_2$ are isomorphic if and only if their characters are equal.

This follows from the proposition and corollary 3 of V, p. 392.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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Cites

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