The q-to-e positivity conjecture for Delta and Xi operators

Let $F$ be a symmetric function with a positive monomial-basis expansion, let $G$ be a symmetric function with a positive Schur-basis expansion, and let $\Delta_F$ and $\Xi$ denote the operators used in the paper. q-to-e positivity conjecture. After the substitution $q\mapsto 1+u$, the symmetric function $\Delta_F\Xi G$ is $e$-positive: the coefficients in its $e$-basis expansion belong to $\mathbb{N}[u,t]$. In particular, the same conclusion should hold when $G$ is $e$-positive. The supplied text notes that the case $\gamma=(k)$ and $G=e_n$ follows from known results, while the general assertion remains conjectural.