Low-dimensional SU3 tensor representations (source code)

= Low-dimensional SU3 tensor representations
{title2=$\mathbf1,\mathbf3,\overline{\mathbf3},\mathbf6,\overline{\mathbf6},\mathbf8$}

The six smallest complex <irreducible representations> of <SU(3)> have <highest weights> $(0,0),(1,0),(0,1),(2,0),(0,2),(1,1)$ and <dimensions> $1,3,3,6,6,8$. Their <Young diagram> row lengths are $(0,0),(1,0),(1,1),(2,0),(2,2),(2,1)$. They are realized by scalars, defining <vectors>, <covectors> (equivalently <antisymmetric tensors> of degree two), upper and lower <symmetric tensors> of degree two, and mixed <tensors> $T^i{}_j$ with zero <trace>, respectively. The <Weyl dimension formula> is $\dim(p,q)=(p+1)(q+1)(p+q+2)/2$. For $p+q\geq3$ this is at least ten, proving that the list exhausts the six smallest <representations>.