4 problems

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 simple affine crystal with extremal vector $u(B^{r,s})$, intrinsic energy $D_{B^{r,s}}$, level $4\operatorname{level}(B^{r,s})4$, and crystal statistic…

Let $B_{\mu}^{t}=B_{\mu}^{t}(\scalebox{0.4}{\ydiagram{2}})$ be the indicated tensor product of crystals, and let the augmentation operation be the operation discussed immediately b…

In types $B_n$ and $D_n$, consider tensor products of KR crystals $B^{k,1}$, represented by KN columns, together with their charge statistic and energy function. Charge-energy conj…