 Tensor square of the A2 representation of highest weight (2,0)

The tensor product of Lie algebra representations decomposes as $R(2,0)\otimes R(2,0)=R(4,0)\oplus R(2,1)\oplus R(0,2)$, of dimensions $15,15,6$. The exterior square is $R(2,1)$ and the symmetric square is $R(4,0)\oplus R(0,2)$. Highest-weight vectors and the dimension formula determine the decomposition.