The gamma-polynomial conjecture for the matroid invariant

Let $x\in G(d,n)$ and let $\gamma_x(s,t)\in\mathbb{Z}[s,t]/\langle s^n,t^n\rangle$ represent the pushforward class $\iota_*q_*p^*[\mathcal{O}_{\overline{Tx}}]$, where $p$ and $q$ are the projections from the relevant partial flag variety and $\iota$ embeds the flag variety as a hypersurface in $\mathbb{P}^{n-1}\times\mathbb{P}^{n-1}$. Let $g_x(t)$ be the associated polynomial invariant and let $c$ be the dimension parameter used in its definition.

Gamma-polynomial conjecture.

$$\gamma_x(s,t)=(-1)^c g_x(-s-t+st).$$

In particular,

$$\gamma_x(s,t)=\gamma_x(t,s).$$

The conjecture would show that $\gamma_x$ contains no information beyond $g_x$ and, together with the duality relation mentioned in the source, would give another proof of $g_x(t)=g_{x^\perp}(t)$. The source gives no resolution evidence, so it remains open.