The rank-three refined Poincaré polynomial formula

Let $N_{3,1}$ be the moduli space of stable rank-three bundles with fixed degree one on a smooth projective curve of genus $g$, and let $\Omega(N_{3,1},q,t)$ denote its refined Poincaré polynomial. The rank-three formula.

$$\Omega(N_{3,1}, q,t) = \frac{1}{(1 - q^2) (1 - q^2 t^2) (1 - q^3 t) (1 - q^3 t^3)} \Big((1 + q^2 t)^{2 g}(1 + q^3 t^2)^{2 g} - q^{4 g - 2} \frac{(1 + q t) (1 - q^3 t)}{1 - t^2} (1 + t)^{2 g} (1 + q t^2)^{2 g} + q^{4 g - 2} t^{2g} \frac{(1 - q^2) (1 + q t + q^2 t^2)}{1-t^2}(1 + q)^{2 g} (1 + t)^{2 g}\Big).$$

The formula is proposed because it satisfies the expected symmetry of the refined Poincaré polynomial, and it has been verified by explicit computations for $g=2,3$; its validity for general genus remains open.