Soliton cellular automaton associated with $G_2^{(1)}$ crystal base

Abstract

We calculate the combinatorial $R$ matrix for all elements of ${\mathcal{B}}_l\otimes {\mathcal{B}}_1$ where ${\mathcal{B}}_l$ denotes the $G_2^{(1)}$-perfect crystal of level $l$, and then study the soliton cellular automaton constructed from it. The solitons of length $l$ are identified with elements of the $A_1^{(1)}$-crystal ${\tilde{\mathcal{B}}}_{3l}$. The scattering rule for our soliton cellular automaton is identified with the combinatorial $R$ matrix for $A_1^{(1)}$-crystals.

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Cited by in corpus (7)

• Categorical relations between Langlands dual quantum affine algebras: Exceptional cases
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$
• Soliton cellular automaton associated with $G_2^{(1)}$ crystal base
• A uniform approach to soliton cellular automata using rigged configurations
• Uniform description of the rigged configuration bijection
• Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$