6 problems

Let $F_\kappa(x;t^{-1})$ denote the relevant flagged LLT-type polynomial and let $w_0\mathcal D_\mu(x)$ be the opposite Demazure character. In the single-row, equal-end-content cas…

Let $\alpha,\beta\in\mathbb{N}^m$, let $\kappa_\alpha$ and $\kappa_\beta$ be Demazure characters, and let $\mathcal{A}_\gamma$ denote the Demazure atom indexed by $\gamma$. Pun's c…

Let $\alpha,\beta\in\mathbb{N}^m$, and let $\kappa_\alpha$ and $\kappa_\beta$ be Demazure characters. For a lower order ideal $\Gamma\subset\mathbb{N}^m$, let $\kappa_\Gamma$ be th…

Flagged Schur module character conjecture. For every northwest diagram $D$,

Assaf–Searles' conjecture. Given a southwest diagram $D$, the Kohnert polynomial ${\mathfrak{K}}_D$ expands non-negatively into Demazure characters.

Let $D$ be a demazure diagram, meaning a finite cell diagram satisfying the demazure condition described in the paper, and let ${\mathfrak K}_D$ denote its Kohnert polynomial. The…