[[Group representation theory MOC]]
# Direct sum of representations

Given two representations $\Gamma : G \to \mathrm{GL}(V)$ and $\tilde{\Gamma} : G \to \mathrm{GL}(W)$,
the **direct sum** $\Gamma \oplus \tilde{\Gamma} : G \to \mathrm{GL}(V \oplus W)$ is defined using the [[Direct sum of linear maps]] as
$$
\begin{align*}
(\Gamma \oplus \tilde{\Gamma})(g) = \Gamma (g) \oplus \tilde{\Gamma}(g)
\end{align*}
$$


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