5 problems

Let ${\boldsymbol\nu},\sigma$ be any flagged LLT indexing data, and let $\mathcal G_{{\boldsymbol\nu},\sigma}[x_1,\ldots,x_l;t]$ be the associated flagged LLT polynomial. If … then…

Let ${\boldsymbol\nu}$ be a tuple of ordinary, non-ragged-right skew diagrams, and let $\sigma$ be the standard compatible permutation. Let…

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 $a$ and $b$ be weak compositions, and let ${\mathfrak{D}}_a$ and ${\mathfrak{D}}_b$ denote the corresponding key polynomials. Let ${\mathfrak{A}}_c$ denote the Demazure atom in…

Let $\alpha$ be a weak composition, and let $A_\alpha$ be the Demazure atom obtained from $x^\alpha$ by applying the operators $\widehat\pi_i=\pi_i-\operatorname{id}$ according to…