Corollary 3

Tag 039J, permanent. Cite it as [Bourbaki, Tag 039J].

Théories spectrales, chapter V, § 1. Représentations unitaires

Let $\varrho_1$ and $\varrho_2$ be finite-dimensional unitary representations of a topological group G. The representations $\varrho_1$ and $\varrho_2$ are isomorphic if and only if $\chi_{\varrho_1}=\chi_{\varrho_2}$ .

This follows from Corollary 2 and A, VIII, p. 389, Prop. 1, b).

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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