Direct sum of representations

Given two representations $Γ : 𝐺 \to G L (𝑉)$ and $˜ Γ : 𝐺 \to G L (𝑊)$ , the direct sum $Γ \oplus ˜ Γ : 𝐺 \to G L (𝑉 \oplus 𝑊)$ is defined using the Direct sum of linear maps as

(Γ \oplus ˜ Γ) (𝑔) = Γ (𝑔) \oplus ˜ Γ (𝑔)

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