The tensor product of the defining representation and its dual is the endomorphism representation. Splitting an endomorphism into its <matrix trace> and traceless part gives
$$
d_1\otimes d_2\cong\mathbf4\otimes\overline{\mathbf4}
=\mathbf1\oplus\mathbf{15}.
$$
In <Dynkin label>[Dynkin labels], the two irreducible summands have highest weights $[0,0,0]$ and $[1,0,1]$.

Solution

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

 Solution

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