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 $R:B^{7,s}\otimes B^{7,s^{\prime }}\to B^{7,s^{\prime }}\otimes B^{7,s}$.

17 pages, 4 figures; v2 added R-matrix description, misc. improvements

References in corpus (12)

• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• X=M for symmetric powers
• Demazure structure inside Kirillov-Reshetikhin crystals
• Perfect Crystals for U_q(D_4^{(3)})
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Path Model for a Level Zero Extremal Weight Module over a Quantum Affine Algebra
• On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models
• Existence of Kirillov--Reshetikhin crystals for multiplicity free nodes
• A uniform approach to soliton cellular automata using rigged configurations
• Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types
• Existence of Kirillov-Reshetikhin crystals of type $G_2^{(1)}$ and $D_4^{(3)}$
• Uniform description of the rigged configuration bijection