Scattering Rule in Soliton Cellular Automaton associated with Crystal Base of $U_q(D_4^{(3)})$

Abstract

In terms of the crystal base of a quantum affine algebra $U_q(\mathfrak{g})$, we study a soliton cellular automaton (SCA) associated with the exceptional affine Lie algebra $\mathfrak{g}=D_4^{(3)}$. The solitons therein are labeled by the crystals of quantum affine algebra $U_q(A_1^{(1)})$. The scatteing rule is identified with the combinatorial $R$ matrix for $U_q(A_1^{(1)})$-crystals. Remarkably, the phase shifts in our SCA are given by {\em 3-times} of those in the well-known box-ball system.

arXiv comment25 pages

References in corpus (4)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Soliton Cellular Automata Associated With Crystal Bases
• Box ball system associated with antisymmetric tensor crystals
• Combinatorial R matrices for a family of crystals : B^{(1)}_n, D^{(1)}_n, A^{(2)}_{2n} and D^{(2)}_{n+1} cases

Cited by in corpus (6)

• 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 $B^{2,s}$