= Adjoint representation of SU(3)
{title2=$\mathbf8=R(1,1)$}
= SU(3) adjoint representation
{c}
{synonym}
The complex <Adjoint representation> of <SU(3)> is the action by conjugation on traceless $3\times3$ matrices. With $H_1=\operatorname{diag}(1,-1,0)$ and $H_2=\operatorname{diag}(0,1,-1)$, its <highest-weight vector> is $E_{13}$ of <Dynkin labels> $(1,1)$. The six off-diagonal matrix units have weights $(2,-1),(-2,1),(-1,2),(1,-2),(1,1),(-1,-1)$, and the two-dimensional <Cartan subalgebra> has weight zero. In coordinates $(h_1,(h_1+2h_2)/\sqrt3)$, the <weight diagram> is a regular hexagon together with a central point of <weight multiplicity> two. This representation describes both the <gluon> colour multiplet and the approximate flavour <baryon octet>, under different physical <SU(3)> symmetries.
Back to article page
