= Kostant multiplicity formula
{c}
{title2=$m_\lambda(\mu)=\sum_{w\in W}\varepsilon(w)p(w(\lambda+\rho)-(\mu+\rho))$}
Multiply the <Weyl character formula> by the <generating series of the Kostant partition function>. In each numerator summand, the coefficient of $e^\mu$ occurs when $\nu=w(\lambda+\rho)-(\mu+\rho)$. Summing those coefficients with the <Weyl group> signs proves the displayed <weight multiplicity> formula. Although $\rho$ need not itself be an integral <group> <weight>, $w\rho-\rho$ is in the <root lattice>, so each partition-function argument is an integral <weight>.
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