9 problems

Let $L_{\lambda\mu}(q)$ denote the $Q$-Kostka polynomial, with $\lambda$ and $\mu$ partitions in the indexing convention of the paper. Positivity conjecture. The $Q$-Kostka polynom…

Connectivity conjecture. For each strict partition $\lambda$ with $\ell(\lambda)\leq n$, the square-root queer crystal $\mathsf{SetDecTab}_n(\lambda)$ is connected and the tableau…

Let $\beta$ be a parameter, let $\beta$-dependent skew functions $j\hspace{-0.2mm}p_{\nu}$ and $j\hspace{-0.2mm}q_{\nu}$ be indexed by strict partitions, and let…

Let $\beta$ be a parameter, let $\beta$-dependent skew functions $ghspace{-0.2mm}p{ u}$ and $ghspace{-0.2mm}q{ u}$ be indexed by strict partitions, and let $u$ be a strict partiti…

Converse CDE conjecture for shifted diagrams. The interval $[\emptyset,\lambda]$ has the CDE property if and only if $\lambda$ is balanced or trapezoidal.

The combinatorial-model conjecture. The restriction of this map to $\overline{\mathcal{T}(\mu^t,\mu,s(\mathcal{T}_\lambda))}$ is a bijection onto…

Let $v$ and $w$ be involution words, and let $\overset{\textsf{O}}\sim$ denote the shifted Hecke equivalence relation. The shifted Hecke insertion algorithm assigns to each word…

Let $n,a,b\geq 0$ and $m\geq 1$. Define the shifted skew shape $\pi=\mathbf{V}(n,a,b,m)$ by … where $\nu^*$ denotes the shifted Young diagram of a strict partition $\nu$. Let…

Ring-generation conjecture. $\mathcal{P}_{\lambda/\mu}$ belongs to the ring generated by the shifted plactic Schur $P$-functions.