The representation with highest weight $[0,0,1]$ is the <dual representation> of $d_1$. Its weights are the negatives of those of $d_1$:
$$
[0,0,1],\quad[0,1,-1],\quad[1,-1,0],\quad[-1,0,0].
$$
Thus $\dim d_2=4$.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-302/4/c/ii/solution