Quivers with subadditive labelings: classification and integrability
Abstract 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 exhibitin...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/131835 |
| _version_ | 1826215934219517952 |
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| author | Galashin, Pavel Pylyavskyy, Pavlo |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Galashin, Pavel Pylyavskyy, Pavlo |
| author_sort | Galashin, Pavel |
| collection | MIT |
| description | Abstract
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. |
| first_indexed | 2024-09-23T16:39:27Z |
| format | Article |
| id | mit-1721.1/131835 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:39:27Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1318352023-01-10T19:38:18Z Quivers with subadditive labelings: classification and integrability Galashin, Pavel Pylyavskyy, Pavlo Massachusetts Institute of Technology. Department of Mathematics Abstract 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. 2021-09-20T17:30:31Z 2021-09-20T17:30:31Z 2019-08-09 2020-09-24T20:47:04Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131835 en https://doi.org/10.1007/s00209-019-02374-x Article 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. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Galashin, Pavel Pylyavskyy, Pavlo Quivers with subadditive labelings: classification and integrability |
| title | Quivers with subadditive labelings: classification and integrability |
| title_full | Quivers with subadditive labelings: classification and integrability |
| title_fullStr | Quivers with subadditive labelings: classification and integrability |
| title_full_unstemmed | Quivers with subadditive labelings: classification and integrability |
| title_short | Quivers with subadditive labelings: classification and integrability |
| title_sort | quivers with subadditive labelings classification and integrability |
| url | https://hdl.handle.net/1721.1/131835 |
| work_keys_str_mv | AT galashinpavel quiverswithsubadditivelabelingsclassificationandintegrability AT pylyavskyypavlo quiverswithsubadditivelabelingsclassificationandintegrability |