Evan Wilson
North Carolina State University, USA / IME-USP
Soliton cellular automaton associated with G_2^(1) crystal base.
Abstract: A cellular automaton is a dynamical system in which points in a space lattice are assigned discrete values which evolve according to a definite rule. Soliton cellular automata (SCA) are a kind of cellular automata which possess stable configurations analogous to solitons in integrable partial differential equation theory. In joint work with Kailash Misra and Masato Okado, we recently computed combinatorial R-matrix of G_2^(1)-crystals and studied the SCA associated with it. The solitons of length l are identified with elements of A_1^(1)-crystals. The scattering rule for the SCA associated with the G_2^(1) crystal base is identified with the combinatorial R matrix for A_1^(1) crystals.