Kirillov-Reshetikhin crystals $B^{7,s}$ for type $E_7^{(1)}$

Abstract

We construct a combinatorial crystal structure on the Kirillov-Reshetikhin crystal $B^{7,s}$ in type $E_7^{(1)}$, where $7$ is the unique node in the orbit of $0$ in the affine Dynkin diagram. We then describe the combinatorial $R$-matrix $R \colon B^{7,s} \otimes B^{7,s'} \to B^{7,s'} \otimes B^{7,s}$.