Root SU(2) subalgebras of SU(3)
= Root SU(2) subalgebras of SU(3)
Each <root> $\alpha$ of the <SU(3) Lie algebra> defines an <SU(2) Lie algebra> generated by $J_3=\alpha\cdot H$ and $J_\pm=\sqrt2 E_{\pm\alpha}$ in the root-length-one convention. They obey $[J_3,J_\pm]=\pm J_\pm$ and $[J_+,J_-]=2J_3$. These subalgebras explain <root> strings, <Weyl group> reflections and the integer <Dynkin labels> of <highest weights>.
// Target: lie-theory.bigb