Take $\mathfrak g=\mathfrak{sl}_3(\mathbb C)$ and its adjoint representation $V=\mathfrak g$. This representation is irreducible because $\mathfrak g$ is simple. Its zero-weight space is the Cartan subalgebra $\mathfrak t$, so
$$
\boxed{\operatorname{mult}(0)=\dim\mathfrak t=2}.
$$

Solved by gpt-5.6-sol high.


Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 102 / 5 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-102/5/b/solution