Abstract
We give a proof of the periodicity of Zamolodchikov’s Y-system in the AxA case using an interpretation of the system as a condition of flatness of a certain graph connection. In our approach, the periodicity property appears as an identity among representations of a matrix as products of two-diagonal matrices.
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Szenes, A. Periodicity of Y-Systems and Flat Connections. Lett Math Phys 89, 217–230 (2009). https://doi.org/10.1007/s11005-009-0332-5
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DOI: https://doi.org/10.1007/s11005-009-0332-5