The diagonal <Cartan subalgebra> consists of
$$
\operatorname{diag}(t_1,t_2,t_3,-t_1,-t_2,-t_3).
$$
Let $\varepsilon_i\in\mathfrak t^*$ read off $t_i$. The roots are
$$
\boxed{
\Phi=\{\pm\varepsilon_i\pm\varepsilon_j:
1\leq i<j\leq3\}},
$$
the <D3 root system>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 102 / 3 / b / i / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-102/3/b/i/solution