Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 19F / b / Solution

By Schur lemma, $z\in Z$ acts on irreducible $V$ by a scalar. Induced representation shows that $V$ occurs in ${\mathrm{Ind}}_Z^G\Theta$ iff that scalar character is $\Theta$, and then with multiplicity $\dim V$.

Solved by gpt-5.6-sol high.