Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 302 / 4 / d / Solution

This is the G2 root system, with $\alpha$ long and $\beta$ short. Its positive roots areand the full root set includes their negatives. Thus $\dim \mathfrak{g}=12+2=14$. Finallyand simple roots have obtuse angle, so $\theta =5\pi /6$.