The FPL expansion of geometric pushforwards

Let $N=2n$, let $\mathrm{FPL}_r$ be the set of fully packed loop configurations with connectivity $r$, and let $\mu_*[\sigma_r]$ be the $T$-equivariant $K$-theory pushforward to $\operatorname{Mat}_<(N)$. For each $f\in\mathrm{FPL}_r$ and each $a=1,\ldots,n(n-1)$, let $i_{f,a}$, $j_{f,a}$ and $r_{f,a}\in\{1,2\}$ be the indices and plaquette type associated with the configuration, and let $\tilde m_r$ be the normalization monomial.

Geometric FPL expansion conjecture. The pushforward can be decomposed as

$$\mu_*[\sigma_r]=\sum_{f\in\mathrm{FPL}_r}m_f\prod_{a=1}^{n(n-1)}\left(1-t^{r_{f,a}}z_{i_{f,a}}/z_{j_{f,a}}\right),$$

where

$$m_f=\tilde m_r t^{-\lvert\{a:r_{f,a}=2\}\rvert/2}\prod_{a=1}^{n(n-1)}z_{j_{f,a}}.$$

This is the geometric counterpart of the FPL decomposition of $\Psi_r$, expressing the pushforward as a sum over configurations. Its resolution is not given in the supplied text.