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- W142444813 abstract "We show that the Yang-Baxter equations for two dimensional vertex models admit as a group of symmetry the infinite discrete group A 2 (1) . The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non trivial algebraic varieties." @default.
- W142444813 created "2016-06-24" @default.
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- W142444813 date "1993-01-01" @default.
- W142444813 modified "2023-09-26" @default.
- W142444813 title "Infinite Discrete Symmetry Group for the Yang-Baxter Equations and their Higher Dimensional Generalizations" @default.
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- W142444813 doi "https://doi.org/10.1007/978-1-4612-0315-5_15" @default.
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