The positivity conjecture for Macdonald superpolynomial Kostka coefficients

Let $H_\Lambda(x,\theta;q,t)$ be the modified Macdonald superpolynomial and let $s_\Omega(x,\theta)$ be the Schur superpolynomial basis. Define the coefficients $K_{\Omega\Lambda}(q,t)$ by

$$H_\Lambda(x,\theta;q,t)=\sum_\Omega K_{\Omega\Lambda}(q,t)s_\Omega(x,\theta).$$

Kostka-positivity conjecture. Every $K_{\Omega\Lambda}(q,t)$ is a polynomial in $q$ and $t$ with nonnegative integer coefficients. The paper proves this conjecture in the stable sector $m\ge n$, while it remains conjectural in the non-stable sector.