Okounkov's Kac polynomial character conjecture for the Maulik–Okounkov Lie algebra

Let $Q$ be an arbitrary finite quiver and fix a dimension vector $\mathbf{d}\in\mathbf{N}^{Q_0}$. Let $\mathtt{a}_{Q,\mathbf{d}}(q)\in\mathbf{Z}[q]$ be Kac's polynomial, counting isomorphism classes of absolutely indecomposable $\mathbf{d}$-dimensional $Q$-representations over $\mathbf{F}_q$. Write $(\mathfrak{g}^{\operatorname{\mathtt{MO}}}_{Q,\mathbf{d}})^k$ for the $k$-th cohomologically graded piece of the $\mathbf{d}$-th graded piece of $\mathfrak{g}^{\operatorname{\mathtt{MO}}}_{Q}$. Okounkov's conjecture. For every such $Q$ and $\mathbf{d}$, there is an equality

$$\sum_{k\in\mathbf{Z}}\dim\left((\mathfrak{g}^{\operatorname{\mathtt{MO}}}_{Q,\mathbf{d}})^k\right)q^{k/2}=\mathtt{a}_{Q,\mathbf{d}}(q^{-1}).$$

The conjecture proposes a Lie-theoretic interpretation of all coefficients of Kac polynomials; the source states that it has been resolved through the theory of BPS Lie algebras, while Kac's constant-term conjecture was proved earlier by Hausel.