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- W2964230478 abstract "In this paper, we use the network solution of the $A_r$ $T$-system to derive that of the unrestricted $A_infty$ $T$-system, equivalent to the octahedron relation. We then present a method for implementing various boundary conditions on this system, which consists of picking initial data with suitable symmetries. The corresponding restricted $T$-systems are solved exactly in terms of networks. This gives a simple explanation for phenomena such as the Zamolodchikov periodicity property for $T$-systems (corresponding to the case $A_elltimes A_r$) and a combinatorial interpretation for the positive Laurent property for the variables of the associated cluster algebra. We also explain the relation between the $T$-system wrapped on a torus and the higher pentagram maps of Gekhtman et al." @default.
- W2964230478 created "2019-07-30" @default.
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- W2964230478 date "2013-01-07" @default.
- W2964230478 modified "2023-10-01" @default.
- W2964230478 title "T-systems with Boundaries from Network Solutions" @default.
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- W2964230478 doi "https://doi.org/10.37236/2645" @default.
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