Restriction multiplicity bound
= Restriction multiplicity bound
For an irreducible complex character $\chi$ of a finite group $G$ and subgroup $H$, write its restriction as $\sum_i d_i\psi_i$. Orthogonality gives $\sum_i d_i^2=|H|^{-1}\sum_{h\in H}|\chi(h)|^2\le|G|/|H|$, because $|G|^{-1}\sum_G|\chi|^2=1$. Equality holds exactly when $\chi$ vanishes outside $H$, since the omitted sum consists of nonnegative terms.