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• W2963535684 abstract "We give the path model solution for the cluster algebra variables of the $T$-system of type $A_r$ with generic boundary conditions. The solutions are partition functions of (strongly) non-intersecting paths on weighted graphs. The graphs are the same as those constructed for the $Q$-system in our earlier work, and depend on the seed or initial data in terms of which the solutions are given. The weights are time-dependent where time is the extra parameter which distinguishes the $T$-system from the $Q$-system, usually identified as the spectral parameter in the context of representation theory. The path model is alternatively described on a graph with non-commutative weights, and cluster mutations are interpreted as non-commutative continued fraction rearrangements. As a consequence, the solution is a positive Laurent polynomial of the seed data." @default.
• W2963535684 created "2019-07-30" @default.
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• W2963535684 date "2009-11-24" @default.
• W2963535684 modified "2023-10-01" @default.
• W2963535684 title "Positivity of the T-System Cluster Algebra" @default.
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• W2963535684 doi "https://doi.org/10.14760/owp-2009-21" @default.
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