Question: Prove that for (mathrm{SU}(2)) symmetry (mathbf{2} otimes mathbf{2} otimes mathbf{2}=mathbf{4} oplus mathbf{2} oplus mathbf{2}), while for (mathrm{SU}(3)) symmetry What is the irrep content of (mathbf{8}

Prove that for $\mathrm{SU}(2)$ symmetry $\mathbf{2} \otimes \mathbf{2} \otimes \mathbf{2}=\mathbf{4} \oplus \mathbf{2} \oplus \mathbf{2}$, while for $\mathrm{SU}(3)$ symmetry

What is the irrep content of $\mathbf{8} \otimes \mathbf{8} \otimes \mathbf{8}$ in $\mathrm{SU}(3)$ ?

= 33 3 10 8 8 1 383=801 303 = 603.

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