= Character expansion of the identity delta
{title2=$\sum_\rho d_\rho\chi_\rho(x)=|G|1_{\{x=e\}}$}
For a <finite group>, the <regular representation> contains $d_\rho$ copies of each <irreducible representation> $\rho$. Its <character of a representation> is $|G|$ at the identity and zero elsewhere. Thus $\sum_\rho d_\rho\chi_\rho(x)=|G|1_{\{x=e\}}$, including the <trivial representation>. This formula converts independent uniform <expectations> into constrained configuration counts.
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