Multiplicity-free restriction
= Multiplicity-free restriction
Restriction of an <irreducible representation> to a <subgroup> is multiplicity-free when its <semisimple representation> decomposition has no repeated irreducible summands. Over the <complex numbers>, for <finite groups>, this is equivalent to the restricted module's endomorphism algebra being commutative. This follows by writing that algebra as a product of <matrix algebras> of sizes equal to the multiplicities.