= Symmetric cubic representation of SU(3)
{title2=$\mathbf{10}=R(3,0)=\operatorname{Sym}^3\mathbb C^3$}
The degree-three monomials $z_1^az_2^bz_3^c$, with $a+b+c=3$, form a basis of this ten-dimensional <highest-weight representation>. Its highest monomial is $z_1^3$, and $E_{21}=z_2\partial_{z_1}$ and $E_{32}=z_3\partial_{z_2}$ generate every basis monomial. Its <Dynkin labels> are $(3,0)$, and the weight of a monomial is $(a-b,b-c)$. In coordinates $(h_1,(h_1+2h_2)/\sqrt3)$, the ten weights form four horizontal rows of lengths $4,3,2,1$, all with <weight multiplicity> one. The <baryon decuplet> realizes this representation of approximate <flavor symmetry>.
// Target: special-relativity.bigb
Back to article page
