Virtual invariants of critical loci in GIT quotients of linear spaces

We use an equivariant version of the localization formula of Jeffrey and Kirwan to prove a formula for virtual invariants $(\text{DT}$, $\chi_y$, $\text{Ell})$ of critical loci in quotients of linear spaces by actions of reductive algebraic groups. In particular we recover formulae for the invariants of critical loci of potentials in moduli spaces of quiver representations predicted by physicists.