dc.contributor.author Di Francesco, Philippe dc.contributor.author Kedem, Rinat dc.date.accessioned 2009-03-20T12:00:41Z dc.date.accessioned 2016-10-05T14:14:13Z dc.date.available 2009-03-20T12:00:41Z dc.date.available 2016-10-05T14:14:13Z dc.date.issued 2009-03-14 dc.identifier.uri http://publications.mfo.de/handle/mfo/1155 dc.description Research in Pairs 2009 en_US dc.description.abstract We give the path model solution for the cluster algebra variables of the $A_r$ T-system 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. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2009,21 dc.title Positivity of the T-system cluster algebra en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2009-21 local.scientificprogram Research in Pairs 2009 local.series.id OWP-2009-21
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