= Tensor cube of the defining SU(3) representation
{title2=$\mathbf3^{\otimes3}=\mathbf{10}\oplus\mathbf8\oplus\mathbf8\oplus\mathbf1$}
The <tensor product of Lie algebra representations> $\mathbf3\otimes\mathbf3$ splits into the symmetric $\mathbf6$ and antisymmetric $\overline{\mathbf3}$. Then $\mathbf6\otimes\mathbf3=\mathbf{10}\oplus\mathbf8$ and $\overline{\mathbf3}\otimes\mathbf3=\mathbf8\oplus\mathbf1$, as <highest-weight character subtraction> verifies. The decuplet is fully symmetric under quark permutations, the singlet fully antisymmetric, and the two octets constitute the two-dimensional mixed permutation multiplicity space. Applying the <Pauli constraint on three-quark flavour multiplets> gives one ground-state spin-one-half octet and one spin-three-halves decuplet.
// Target: physics.bigb
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