Harder-Narasimhan filtrations and zigzag persistence
<p>We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type A quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistenc...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2023
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| _version_ | 1797111585751171072 |
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| author | Fersztand, M Nanda, V Tillmann, U |
| author_facet | Fersztand, M Nanda, V Tillmann, U |
| author_sort | Fersztand, M |
| collection | OXFORD |
| description | <p>We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type A quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.</p> |
| first_indexed | 2024-03-07T08:10:55Z |
| format | Journal article |
| id | oxford-uuid:4adc2ed9-9794-4ca2-bd0f-5e622a140a29 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:10:55Z |
| publishDate | 2023 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:4adc2ed9-9794-4ca2-bd0f-5e622a140a292023-12-01T08:20:08ZHarder-Narasimhan filtrations and zigzag persistenceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4adc2ed9-9794-4ca2-bd0f-5e622a140a29EnglishSymplectic ElementsElsevier2023Fersztand, MNanda, VTillmann, U<p>We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result establishes that for representations of affine type A quivers, there is a precise relationship between the associated Harder-Narasimhan filtration and the barcode of the periodic zigzag persistence module obtained by unwinding the underlying quiver.</p> |
| spellingShingle | Fersztand, M Nanda, V Tillmann, U Harder-Narasimhan filtrations and zigzag persistence |
| title | Harder-Narasimhan filtrations and zigzag persistence |
| title_full | Harder-Narasimhan filtrations and zigzag persistence |
| title_fullStr | Harder-Narasimhan filtrations and zigzag persistence |
| title_full_unstemmed | Harder-Narasimhan filtrations and zigzag persistence |
| title_short | Harder-Narasimhan filtrations and zigzag persistence |
| title_sort | harder narasimhan filtrations and zigzag persistence |
| work_keys_str_mv | AT fersztandm hardernarasimhanfiltrationsandzigzagpersistence AT nandav hardernarasimhanfiltrationsandzigzagpersistence AT tillmannu hardernarasimhanfiltrationsandzigzagpersistence |