Solution
= Solution
Choose positive roots $\Phi^+$ and let
$$
\rho=\frac12\sum_{\alpha\in\Phi^+}\alpha
$$
be the <Weyl vector>. For a <dominant integral weight> $\lambda$, the <Weyl dimension formula> is
$$
\boxed{\dim V(\lambda)
=\prod_{\alpha\in\Phi^+}
\frac{\langle\lambda+\rho,\alpha^\vee\rangle}
{\langle\rho,\alpha^\vee\rangle}}.
$$
Here $\alpha^\vee$ is the coroot and $\langle\ ,\ \rangle$ is the natural weight-coroot pairing.