4 problems

Let $(V,\widehat{V})$ and $(V',\widehat{V}')$ be simple aligned virtual crystals, where $V$ and $V'$ are $X$-crystals and the hatted crystals are $Y$-crystals. Let … be the type…

Let $4\mathfrak{g}4$ be of type $D_{n+1}^{(2)}$, $A_{2n}^{(2)}$, $A_{2n}^{(2)\dagger}$, or $C_n^{(1)}$, let $1\leq r\leq n$ and $s\geq1$, and let $V^{r,s}$ be the virtual crystal w…

For $4\mathfrak{g}4$ of type $D_{n+1}^{(2)}$, $A_{2n}^{(2)}$, $A_{2n}^{(2)\dagger}$, or $C_n^{(1)}$, let $V^{r,s}$ be the virtual crystal embedded in an ambient type…

Let $B^{r,s}$ be a Kirillov--Reshetikhin crystal for an affine type, and let $\phi$ and $(\gamma_a)_{a\in I}$ be the folding and scaling data defining virtual crystals. Define … Vi…