Use Table 7.1 and Theorems 7.1 -7.2 to construct root diagrams for the rank-2 compact algebras \(\mathrm{SU}(3)\) and \(\mathrm{SO}(5)\).

Data from Table 7.1

Data from Theorem 7.1

If α is a non-vanishing root, then −α is a root also.

Data from Theorem 7.2

Table 7.1. Possible relative root vector angles and lengths [72] cos (a,) e(a,)+ a. n = 2 n' = =2 n' n -B 134 -2 0, 180 2 2 30, 150 3 1 3 1 3 3 #2 45, 135 2 1 2 2 CAT 60, 120 1 1 1 0 90 0 0 indeterminate 180 is redundant by Theorem 7.1 and 0 is excluded by uniqueness of roots.