Combinatorial R-matrices for Kirillov--Reshetikhin crystals of type D^{(1)}_n, B^{(1)}_n, A^{(2)}_{2n-1}

Abstract

We calculate the image of the combinatorial R-matrix for any classical highest weight element in the tensor product of Kirillov--Reshetikhin crystals $B^{r,k}\otimes B^{1,l}$ of type $D_n^{(1)},B_n^{(1)},A_{2n-1}^{(2)}$. The notion of $\pm$-diagrams is effectively used for the identification of classical highest weight elements in $B^{1,l}\otimes B^{r,k}$.

27 pages

References in corpus (4)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• Energy Functions in Box Ball Systems
• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)

Cited by in corpus (2)

• Affine crystal structure on rigged configurations of type D_n^(1)
• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$