5 problems

Let $n$ be a positive integer, let $\lambda=(\lambda_1\geq\cdots\geq\lambda_n\geq 0)$ be a partition, and consider the multispecies totally asymmetric simple exclusion process (TAS…

Let $B$ be a tensor product of Kirillov--Reshetikhin crystals of affine type. Let $\operatorname{RC}(B)$ be the corresponding set of rigged configurations, let $\eta$ interchange r…

Let $B^{r,s}$ and $B^{r',s'}$ be KR crystals of type $D_4^{(3)}$, and let the virtual combinatorial $R$-matrix be induced by restriction of the type $D_4^{(1)}$ combinatorial $R$-m…

Let $B^{r,s}$ and $B^{r',s'}$ be KR crystals, and let … be the combinatorial $R$-matrix, characterized by sending $u_{r,s}\otimes u_{r',s'}$ to $u_{r',s'}\otimes u_{r,s}$, where…

Let $(\nu,J)\in\operatorname{RC}(B)$, where $B=B_1\otimes B_2$ is a two-fold tensor product of Kirillov--Reshetikhin crystals, and let $B'=B_2\otimes B_1$ be the tensor product wit…