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

TL;DR

This paper computes the combinatorial R-matrix for tensor products of Kirillov--Reshetikhin crystals of specific types, using $\

Contribution

It introduces an effective method using $"+-\" diagrams to identify classical highest weight elements in these tensor products.

Findings

Explicit formulas for the R-matrix images are derived.

$\

paper_type":"method"}}

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 $D^{(1)}_n, B^{(1)}_n, A^{(2)}_{2n-1}$. The notion of $\pm$-diagrams is effectively used for the identification of classical highest weight elements in $B^{1,l}\otimes B^{r,k}$.