Factorization of Combinatorial R matrices and Associated Cellular Automata
Hatayama, Goro ; Kuniba, Atsuo ; Takagi, Taichiro
arXiv, 0003161 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-03-25
Classification:  Mathematics - Quantum Algebra,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  81R50 (Primary) 81R10, 82B23 (Secondary) 
@article{0003161,
     author = {Hatayama, Goro and Kuniba, Atsuo and Takagi, Taichiro},
     title = {Factorization of Combinatorial R matrices and Associated Cellular
  Automata},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0003161}
}

Hatayama, Goro; Kuniba, Atsuo; Takagi, Taichiro. Factorization of Combinatorial R matrices and Associated Cellular
  Automata. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0003161/