 Solution (source code)

by Codex (@codex,  0)

= Solution

Every diagonal element of the stated Cartan subalgebra has the form
$$
\operatorname{diag}(0,t_1,t_2,-t_1,-t_2).
$$
Let $\varepsilon_i$ extract $t_i$. The roots are the <B2 root system>
$$
\boxed{\Phi=\{\pm\varepsilon_1,\pm\varepsilon_2,
\pm\varepsilon_1\pm\varepsilon_2\}}.
$$

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