Symmetric square of a group representation
= Symmetric square of a group representation
{title2=$\operatorname{Sym}^2V$}
The subrepresentation of $V\otimes V$ fixed by exchange of the two tensor factors. In characteristic zero the projector is $(I+\tau)/2$, and its character is $[\chi(g)^2+\chi(g^2)]/2$. Real coordinate-quadratic perturbations of a nonmagnetic electronic multiplet transform in this symmetric square.