= Symmetric spin-flavour SU6 representation
{title2=$\mathbf{56}=(\mathbf{10},\mathbf4)\oplus(\mathbf8,\mathbf2)$}
Three light <quarks> have a six-dimensional single-quark spin-flavour space $\mathbb C^3\otimes\mathbb C^2$. A symmetric spatial ground state and the antisymmetric <three-quark colour singlet> require the symmetric cube of that space. Its dimension is $\binom83=56$, and restriction to flavour $SU(3)$ and spin $SU(2)$ gives a <baryon decuplet> of spin $3/2$ and a <baryon octet> of spin $1/2$. The two mixed-permutation multiplicity spaces pair once in the symmetric sector, explaining why the two flavour-octet copies in the unconstrained <tensor> cube do not represent two distinct ground-state octets.
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