Figure 48

Figure 48: The representation 152 of 𝔰𝔩(3,ℝ) appearing at level two in the decomposition of the adjoint representation of AE3 into representations of 𝔰𝔩(3,ℝ ). The lowest leftmost node is the lowest weight of the representation, corresponding to the real root Λ(2) = 2α + α 1 2 of AE 3. This representation has outer multiplicity one.