11 problems

For two shifted shapes $\lambda$ and $\mu$, let $\lambda\cup\mu$ be the partition obtained by rearranging all parts of $\lambda$ and $\mu$ in weakly decreasing order, and write … D…

Let $\lambda/\mu$ and $\nu/\rho$ be skew shifted shapes. For partitions, define componentwise operations … and extend them to skew shifted shapes by…

Let $P_n$ be the algebra containing the element $f$, let $\mathrm{Pfaf}'_D$ denote the diagram pfaffinants, and let $A_{\lambda/\mu}$ be a generalized $Q$-Jacobi-Trudi matrix assoc…

Let $D$ and $E$ be shifted skew shapes. A frayed ribbon is a shifted near-ribbon containing two squares on the staircase, and let $D^a$ denote the antipodal reflection of $D$ acros…

KdV-characterization conjecture. The set of Hirota bilinear equations

Generalized BGW hypergeometricity conjecture. The generalized BGW tau-function, after a simple rescaling of times, is a hypergeometric solution of the BKP hierarchy.

Let $\operatorname{DP}$ denote the set of strict partitions, let $Q_\lambda({\bf t})$ be the normalized Schur Q-function, and let $\delta_{k,j}$ denote the specialization with valu…

Let $D=D_1\cup\cdots\cup D_r$ be a ribbon with connected components $D_i$, for $i=1,\dots,r$, and let $\mathfrak{r}_D$ denote its ribbon Schur $Q$-function. Componentwise p-positiv…

Let $D$ be a connected ribbon, let $\mathfrak{B}$ be the set of basic blocks, and let $\mathfrak{r}_D$ denote its ribbon Schur $Q$-function. For compositions…

Conjectural skew Littlewood–Richardson rule. The product of skew Schur $Q$-functions should satisfy

Let $\lambda$ be a partition with distinct parts. The srank of $\lambda$ is the number of bars in a minimal bar tableau of shape $\lambda$. Let $Q_{\lambda}$ be Schur's $Q$-functio…