Solution
= Solution
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
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 $\dim d_2=4$.