Character of a tensor product
= Character of a tensor product
{title2=$\chi_{V\otimes W}=\chi_V\chi_W$}
For finite-dimensional <group representations>, the <character> of their <tensor product> is the pointwise product of their <characters>. In a <tensor-product basis>, the diagonal entries of $A\otimes B$ are $A_{ii}B_{jj}$, so their sum is $(\operatorname{tr}A)(\operatorname{tr}B)$. This gives a direct route from a <character table> to tensor-product decompositions.