Write an element of the diagonal <Cartan subalgebra> as
$$
t=\operatorname{diag}(t_1,t_2,t_3,-t_1,-t_2,-t_3)
$$
and define the <linear functionals> $\varepsilon_i(t)=t_i$. The <root-space decomposition> of the <Symplectic Lie algebra> $\mathfrak{sp}_6(\mathbb C)$ then has the <C3 root system>
$$
\boxed{\Phi=\{\pm\varepsilon_i\pm\varepsilon_j:1\leq i<j\leq3\}\cup\{\pm2\varepsilon_i:1\leq i\leq3\}.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 102 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-102/2/a/solution