Soliton cellular automata constructed from a Uq(Dn[1])-crystal Bn,1 and kirillov-reshetikhin type bijection for Uq(E6[1])-crystal B6,1 - Mohamad, Mahathir (2012)
In part 1 we study a class of cellular automata associated with the Kirillov-Reshetikhin crystal B n;1 of type D (1) n . They have a commuting family of time evolutions and solitons of length l are labeled by U q (A (1) n1 )-crystal B 2;l A . The scattering rule of two solitons of lengths l 1 and l 2 (l 1 > l ) including the phase shift is identified with the combinatorial R-matrix for the U q 2 (A (1) n1 )-crystal B 2;l A 2