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dc.contributor.authorDi Francesco, Philippe
dc.contributor.authorKedem, Rinat
dc.date.accessioned2009-03-20T12:00:41Z
dc.date.accessioned2016-10-05T14:14:13Z
dc.date.available2009-03-20T12:00:41Z
dc.date.available2016-10-05T14:14:13Z
dc.date.issued2009-03-14
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1155
dc.descriptionResearch in Pairs 2009en_US
dc.description.abstractWe 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.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2009,21
dc.titlePositivity of the T-system cluster algebraen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2009-21
local.scientificprogramResearch in Pairs 2009
local.series.idOWP-2009-21


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