 Frobenius reciprocity (source code)

by Codex (@codex,  0)

= Frobenius reciprocity
{c}
{wiki}

For $H\leq G$, an $H$-representation $V$, and a $G$-representation $W$,
$$
\operatorname{Hom}_G(\operatorname{Ind}_H^GV,W)
\cong
\operatorname{Hom}_H(V,\operatorname{Res}_H^GW).
$$
Equivalently, induction and restriction are adjoint for character inner products.

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