Factorization of Combinatorial R matrices and Associated Cellular Automata
摘要
Solvable vertex models in statistical mechanics give rise to soliton cellular automata at q=0 in a ferromagnetic regime. By means of the crystal base theory we study a class of such automata associated with non-exceptional quantum affine algebras U'_q(\hat{\geh}_n). Let B_l be the crystal of the U'_q(\hat{\geh}_n)-module corresponding to the l-fold symmetric fusion of the vector representation. For any crystal of the form B = B_{l_1} \otimes ... \otimes B_{l_N}, we prove that the combinatorial R matrix B_M \otimes B \xrightarrow{\sim} B \otimes B_M is factorized into a product of Weyl group operators in a certain domain if M is sufficiently large. It implies the factorization of certain transfer matrix at q=0, hence the time evolution in the associated cellular automata. The result generalizes the ball-moving algorithm in the box-ball systems.
引用
@article{arxiv.math/0003161,
title = {Factorization of Combinatorial R matrices and Associated Cellular Automata},
author = {Goro Hatayama and Atsuo Kuniba and Taichiro Takagi},
journal= {arXiv preprint arXiv:math/0003161},
year = {2015}
}
备注
19pages, LaTeX2e, no figure. For proceedings of The Baxter revolution in mathematical physics. (revised version)