Direct sum of group representations
= Direct sum of group representations
{title2=$R\oplus S$}
For <group representations> $R:G\to GL(V)$ and $S:G\to GL(W)$, their direct sum acts on the <direct sum of vector spaces> by $(R\oplus S)(g)(v,w)=(R(g)v,S(g)w)$. Its <character> and <Dynkin index>, when defined, are the sums of those of the two summands.