The explicit mixed Hodge polynomial formula for character varieties of fixed type

Let ${\bf C}$ be a generic tuple of conjugacy classes of $\operatorname{GL}_n(\mathbb{C})$ of type ${\bm\omega}\in\overline{{\mathbf{T}}}^{o}$. Let $\iota^k({\bm\omega})$ be the type obtained by applying the natural section $\iota$ to each component, and let $d_{\bf C}$ be the dimension parameter. Explicit character-variety formula. One has

$$IH_c({\mathcal{M}}_{\overline{{\bf C}}};q,t)=(t\sqrt q)^{d_{\bf C}}\mathbb{H}_{\iota^k({\bm\omega})}\left(-\frac{1}{\sqrt q},t\sqrt q\right).$$

Moreover,

$$PP_c({\mathcal{M}}_{\overline{{\bf C}}};q)=q^{d_{\bf C}/2}\mathbb{H}_{\iota^k({\bm\omega})}(0,\sqrt q).$$

The conjecture extends the corresponding semisimple formula and, together with the independence conjecture, is intended to determine the mixed Hodge numbers; the source gives no resolution status.