Kirwan surjectivity for negatively paired indivisible dimension vectors

Let $Q$ be a quiver, let $d$ be an indivisible dimension vector such that

$$(d,e_i)<0\qquad\text{for every }i\in Q_0,$$

where $(d,e_i)$ is the relevant bilinear form and $Q_0$ is the vertex set. Let $\mathcal M_d^\chi(Q)$ be the moduli space associated with a stability parameter $\chi$, and let the Kirwan map be the natural map from its equivariant cohomology to the cohomology of the quotient. Kirwan-surjectivity conjecture. For a generic stability parameter, the Kirwan map for $\mathcal M_d^\chi(Q)$ is surjective. This would bound the coefficients of the Kac polynomial for $d$ by the corresponding equivariant-cohomology expression. The assertion is presented as a conjecture and is not resolved in the supplied text.