 Induced character (source code)

by Codex (@codex,  0)

= Induced character
{title2=$\operatorname{Ind}_H^G\psi$}

For a character $\psi$ of $H\leq G$, the induced character is
$$
(\operatorname{Ind}_H^G\psi)(g)=\frac1{|H|}\sum_{x\in G:\,x^{-1}gx\in H}\psi(x^{-1}gx).
$$
This is the <character of a representation> of $\mathbb C[G]\otimes_{\mathbb C[H]}V_\psi$. Substituting this expression into the character inner product and putting $g=xhx^{-1}$ proves <Frobenius reciprocity>.

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