3 problems

Let … be a tensor product of KR crystals, with virtualization map $v$ to the corresponding virtual crystal, and let $\Phi$ be the rigged-configuration bijection. Virtualization com…

Let $\widetilde{B}^{3,s}$ be the crystal represented by tableaux in a $3\times s$ rectangle with classical decomposition … Let $\widehat{B}^{3,s}$ and $\widehat{B}^{4,s}$ be the re…

Let $\mathfrak{g}$ be of type $D_4^{(3)}$, and let $\widehat{\mathfrak{g}}$ be the folded type $D_4^{(1)}$. Write $\widehat{B}^{r,s}$ for KR crystals of type $D_4^{(1)}$. KR virtua…