dorsal/arxiv
View SchemaSoliton Cellular Automata Associated With Crystal Bases
| Authors | Goro Hatayama, Atsuo Kuniba, Taichiro Takagi |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9907020 |
| URL | https://arxiv.org/abs/solv-int/9907020 |
| DOI | 10.1016/S0550-3213(00)00105-X |
| Journal | Nuclear Physics B577[PM](2000) 619-645 |
Abstract
We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U'_q(\hat{\geh}_n). They have solitons labeled by crystals of the smaller algebra U'_q(\hat{\geh}_{n-1}). We prove stable propagation of one soliton for \hat{\geh}_n = A^{(2)}_{2n-1}, A^{(2)}_{2n}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}. For \gh_n = C^{(1)}_n, we also prove that the scattering matrices of two solitons coincide with the combinatorial R matrices of U'_q(C^{(1)}_{n-1})-crystals.
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"abstract": "We introduce a class of cellular automata associated with crystals of\nirreducible finite dimensional representations of quantum affine algebras\nU\u0027_q(\\hat{\\geh}_n). They have solitons labeled by crystals of the smaller\nalgebra U\u0027_q(\\hat{\\geh}_{n-1}). We prove stable propagation of one soliton for\n\\hat{\\geh}_n = A^{(2)}_{2n-1}, A^{(2)}_{2n}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n\nand D^{(2)}_{n+1}. For \\gh_n = C^{(1)}_n, we also prove that the scattering\nmatrices of two solitons coincide with the combinatorial R matrices of\nU\u0027_q(C^{(1)}_{n-1})-crystals.",
"arxiv_id": "solv-int/9907020",
"authors": [
"Goro Hatayama",
"Atsuo Kuniba",
"Taichiro Takagi"
],
"categories": [
"solv-int",
"math.QA",
"nlin.SI"
],
"doi": "10.1016/S0550-3213(00)00105-X",
"journal_ref": "Nuclear Physics B577[PM](2000) 619-645",
"title": "Soliton Cellular Automata Associated With Crystal Bases",
"url": "https://arxiv.org/abs/solv-int/9907020"
},
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