Mackey irreducibility criterion
= Mackey irreducibility criterion
{c}
For an irreducible $H$-representation $V$, the induced representation $\operatorname{Ind}_H^GV$ is irreducible exactly when, for every nonidentity double coset representative $x\in H\backslash G/H$, the restrictions of $V$ and its $x$-conjugate to $H\cap xHx^{-1}$ have inner product zero.