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dc.contributor.authorGalashin, Pavel
dc.contributor.authorPylyavskyy, Pavlo
dc.date.accessioned2021-09-20T17:30:31Z
dc.date.available2021-09-20T17:30:31Z
dc.date.issued2019-08-09
dc.identifier.urihttps://hdl.handle.net/1721.1/131835
dc.description.abstractAbstract Strictly subadditive, subadditive and weakly subadditive labelings of quivers were introduced by the second author, generalizing Vinberg’s definition for undirected graphs. In our previous work we have shown that quivers with strictly subadditive labelings are exactly the quivers exhibiting Zamolodchikov periodicity. In this paper, we classify all quivers with subadditive labelings. We conjecture them to exhibit a certain form of integrability, namely, as the T-system dynamics proceeds, the values at each vertex satisfy a linear recurrence. Conversely, we show that every quiver integrable in this sense is necessarily one of the 19 items in our classification. For the quivers of type $${\hat{A}} \otimes A$$ A ^ ⊗ A we express the coefficients of the recurrences in terms of the partition functions for domino tilings of a cylinder, called Goncharov–Kenyon Hamiltonians. We also consider tropical T-systems of type $${\hat{A}} \otimes A$$ A ^ ⊗ A and explain how affine slices exhibit solitonic behavior, i.e. soliton resolution and speed conservation. Throughout, we conjecture how the results in the paper are expected to generalize from $${\hat{A}} \otimes A$$ A ^ ⊗ A to all other quivers in our classification.en_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttps://doi.org/10.1007/s00209-019-02374-xen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleQuivers with subadditive labelings: classification and integrabilityen_US
dc.typeArticleen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2020-09-24T20:47:04Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag GmbH Germany, part of Springer Nature
dspace.embargo.termsY
dspace.date.submission2020-09-24T20:47:04Z
mit.licensePUBLISHER_POLICY
mit.metadata.statusAuthority Work and Publication Information Needed


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