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

One root basis isAll roots have the same length. The nonzero inner products are $({\alpha }_1,{\alpha }_2)=({\alpha }_1,{\alpha }_3)=-1$, so the labeled Dynkin diagram isIt is the three-node $A_3$ diagram.