Kostant partition function
= Kostant partition function
{c}
{title2=$P(\nu)$}
{wiki}
The Kostant partition function $P(\nu)$ counts the ways to express a weight $\nu$ as a nonnegative integer combination of positive roots. By the <Poincare-Birkhoff-Witt theorem>, $P(\lambda-\mu)$ is the multiplicity of the weight $\mu$ in the <Verma module> $M(\lambda)$.