Remark 3

Tag 00O6, permanent. Cite it as [Bourbaki, Tag 00O6].

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

Let $\pi_1$ and $\pi_2$ be linear representations of $G$ in finite-dimensional vector spaces over $K$ . For $i = 1, 2$ , let $\pi_i'$ be a representation related to $\pi_i$ through $\varphi$ . We have

\dim_K \operatorname{Hom}_K(\pi_1, \pi_2) = \dim_{K'} \operatorname{Hom}_{K'}(\pi_1', \pi_2') .

The proof follows that of Corollary VIII, p. 410, by reducing to the case when the

\pi_i

(and therefore the

\pi_i'

) are simple.

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. 410