Triality (SU(3)) (source code)

= Triality
{disambiguate=SU(3)}
{title2=$(a+2b)\bmod3$}

= SU(3) triality
{c}
{synonym}

The central element $\omega I$ of <SU(3)>, with $\omega=e^{2\pi i/3}$, acts on an irreducible representation of <Dynkin labels> $(a,b)$ as $\omega^{a+2b}$. This residue is its triality. In a tensor realization the representation has $a+2b$ fundamental boxes, and a complete column of three is a singlet; removing such columns preserves the residue. Tensor products add trialities and complex conjugation reverses them.