For a dominant integral <highest weight> $\lambda$, the <Weyl dimension formula> is
$$
\boxed{\dim V(\lambda)=\prod_{\alpha\in\Phi^+}
\frac{\langle\lambda+\rho,\alpha^\vee\rangle}
{\langle\rho,\alpha^\vee\rangle},}
$$
where $\Phi^+$ is the chosen <positive system of a root system>, $\alpha^\vee$ is a <coroot>, and $\rho$ is the <Weyl vector>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 102 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-102/4/a/solution