Quotient representation

Given a group representation $ρ : G \to G L (V)$ , a quotient representation is a representation of $G$

\tilde{ρ} : G \to G L (V / W),

where $W$ is an invariant vector subspace of $V$ , defined by

\tilde{ρ} (g) : v + W \mapsto ρ (g) (v) + W .