Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 302 / 4 / c / i

Starting from $[1,0,0]$ and applying the simple-root lowerings gives the four weightsEach has weight multiplicity one, so $d_1$ is the four-dimensional defining representation of $A_3\cong {\mathfrak{sl}}_4(\mathbb{C})$.