# Compute formal character of semisimple Lie algebras.

Let $\mathfrak{g}$ be a semisimple Lie algebra and $V_{\lambda}$ be the irreducible $\mathfrak{g}$-module with highest weight $\lambda$. Are there some softwares which can compute the formal character $ch(V_{\lambda})=\sum_{\mu}dim(V_{\mu})e(\mu)$ explicitly? We can use Weyl formula. But it is difficult to compute the result in practice. Thank you very much.

• Maybe it's worth pointing out that Weyl's conceptually elegant character formula is almost never useful for actual computations of weight multiplicities. Algorithms for weight multiplicities are typically based on some variant of Freudenthal's formula, which doesn't require working simultaneously with all elements of the Weyl group. (Still, it's a problem to track down easily usable software, since people tend to develop systems and then move on to other things.) – Jim Humphreys Aug 26 '11 at 21:30