Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models
A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type ₙ or type ₂ₙ₊₁ symmetries. These recurrence relations describe how to add a single parameter to specific subsets of Bethe parameters, expressing the resulting...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214090 |
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| Cite this: | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models. Andrii Liashyk, Stanislav Pakuliak and Eric Ragoucy. SIGMA 21 (2025), 078, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862724012976635904 |
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| author | Liashyk, Andrii Pakuliak, Stanislav Ragoucy, Eric |
| author_facet | Liashyk, Andrii Pakuliak, Stanislav Ragoucy, Eric |
| citation_txt | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models. Andrii Liashyk, Stanislav Pakuliak and Eric Ragoucy. SIGMA 21 (2025), 078, 28 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type ₙ or type ₂ₙ₊₁ symmetries. These recurrence relations describe how to add a single parameter to specific subsets of Bethe parameters, expressing the resulting Bethe vector as a linear combination of monodromy matrix entries that act on Bethe vectors which do not depend on . We refer to these recurrence relations as rectangular because the monodromy matrix entries involved are drawn from the upper-right rectangular part of the matrix. This construction is achieved within the framework of the zero-mode method.
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| first_indexed | 2026-03-21T06:44:03Z |
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| id | nasplib_isofts_kiev_ua-123456789-214090 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T06:44:03Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
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| spelling | Liashyk, Andrii Pakuliak, Stanislav Ragoucy, Eric 2026-02-19T11:09:43Z 2025 Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models. Andrii Liashyk, Stanislav Pakuliak and Eric Ragoucy. SIGMA 21 (2025), 078, 28 pages 1815-0659 2020 Mathematics Subject Classification: 82B23; 81R12; 17B37; 17B80 arXiv:2412.05224 https://nasplib.isofts.kiev.ua/handle/123456789/214090 https://doi.org/10.3842/SIGMA.2025.078 A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type ₙ or type ₂ₙ₊₁ symmetries. These recurrence relations describe how to add a single parameter to specific subsets of Bethe parameters, expressing the resulting Bethe vector as a linear combination of monodromy matrix entries that act on Bethe vectors which do not depend on . We refer to these recurrence relations as rectangular because the monodromy matrix entries involved are drawn from the upper-right rectangular part of the matrix. This construction is achieved within the framework of the zero-mode method. Weare grateful to Alexander Molev for fruitful discussions on embeddings in Yangian algebras. We would like to acknowledge the anonymous referees for their numerous relevant remarks, which contributed to improving the paper. S.P. acknowledges the support of the PAUSE Programme and hospitality at LAPTh, where this work was done. The research of A.L. was supported by the Beijing Natural Science Foundation (IS24006) and the Beijing Talent Program. A.L. is also grateful to the CNRS PHYSIQUE for support during his visit to Annecy in the course of this investigation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models Article published earlier |
| spellingShingle | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models Liashyk, Andrii Pakuliak, Stanislav Ragoucy, Eric |
| title | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models |
| title_full | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models |
| title_fullStr | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models |
| title_full_unstemmed | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models |
| title_short | Rectangular Recurrence Relations in ₙ and ₂ₙ₊₁ Invariant Integrable Models |
| title_sort | rectangular recurrence relations in ₙ and ₂ₙ₊₁ invariant integrable models |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214090 |
| work_keys_str_mv | AT liashykandrii rectangularrecurrencerelationsinnand2n1invariantintegrablemodels AT pakuliakstanislav rectangularrecurrencerelationsinnand2n1invariantintegrablemodels AT ragoucyeric rectangularrecurrencerelationsinnand2n1invariantintegrablemodels |