Answer by guest for Proof that the induced class function $\theta^G$ is a...
Because the trace is an additive invariant of a representation. If $V= \bigoplus a_iV_i$ is a $G$-module, then for each $g\in G$ $$\chi_V(g) = Tr(\pi(g)) = Tr(\sum_i a_i\pi_i(g)) = \sum a_i...
View ArticleProof that the induced class function $\theta^G$ is a character if $\theta$...
In these lecture notes by Daniel Bump on Induced Characters I have a question on the proof of Theorem 2.5.1. If $H$ is a subgroup of the finite group $G$ and $(\pi, V)$ a representation of $H$, i.e. a...
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