# Subrepresentation

In representation theory in mathematics, a subrepresentation of a representation ${\displaystyle (\pi ,V)}$ of a group G is a representation ${\displaystyle (\pi |_{W},W)}$ such that W is a vector subspace of V and ${\displaystyle \pi |_{W}(g)=\pi (g)|_{W}}$.
If ${\displaystyle (\pi ,V)}$ is a representation of G, then there is the trivial subrepresentation:
${\displaystyle V^{G}=\{v\in V|\pi (g)v=v,\,g\in G\}.}$