Corollary 1

Tag 00O3, permanent. Cite it as [Bourbaki, Tag 00O3].

Algebra, VIII, p. 420, § 21. Linear Representations of Finite Groups

The mapping $\varphi_G$ is a ring isomorphism from $R_K(G)$ to $R_{K'}(G)$ . For every finite-dimensional representation $\pi$ of $G$ in a $K$ -vector space, we have $\varphi_G([\pi]) = [\pi']$ , where $\pi'$ is a representation related to $\pi$ through $\varphi$ .

This follows from the semisimplicity of the representations of $G$ and property b) of VIII, p. 416.

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.

Cited by

Nothing.

Cites

VIII, p. 416