8 problems

Type D affine crystal conjecture. If $B^{r,s}$ exists, then

Let $D$ be a $\pm$ diagram of shape $\Lambda/\lambda$ whose ambient $r\times s$ rectangle has complement of $\Lambda$ tiled by vertical dominos. Let $m_{i}^{\circ}$, $m_{i}^{+}$,…

Let $G$ be one of the classical groups and let $\mu^{(1)},...,\mu^{(r)}$ and $\lambda$ index the corresponding $q$-analogue $\frak{D}_{\mu^{(1)},...,\mu^{(r)}}^{\lambda,G}(q)$ of a…

Let $\mathfrak{g}$ be of affine type other than $A_n^{(1)}$, with parameters $N_0$, $\kappa$, $c_a$, and $t_a$ as defined in the source. For a classically lowest weight element…

Let $\mathfrak{g}$ be of affine type other than $A_n^{(1)}$. Let $N_0$ and $\kappa$ be as in the source, and let $(c_a)_{a\in I}$ and $(t_a)_{a\in I}$ be the Kac-label data and ass…

Let … be a tensor product of type $D_4^{(3)}$ KR crystals, and let $\operatorname{RC}(B)$ be its rigged-configuration set equipped with the conjectural affine crystal operators. Af…

Let $\mathfrak{g}$ be of type $D_{n+1}^{(1)}$, and let $\widetilde{B}^{n,s}$ be the affine crystal constructed by the stated classical decomposition and affine operators. Spin-crys…

Schilling–Shimozono conjecture. For $\diamondsuit\in\{(1),(2),(1,1)\}$,