A-Type Open SL(2, ℂ) Spin Chain
For the noncompact open SL(2, ℂ) spin chain, the eigenfunctions of the special matrix element of the monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter -operators, -operator, and raising operators obtained by reduction from the -operator. The calcul...
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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/123456789/214186 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A-Type Open SL(2, ℂ) Spin Chain. Pavel V. Antonenko, Sergey É. Derkachov and Pavel A. Valinevich. SIGMA 21 (2025), 107, 48 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862576322117632000 |
|---|---|
| author | Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. |
| author_facet | Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. |
| citation_txt | A-Type Open SL(2, ℂ) Spin Chain. Pavel V. Antonenko, Sergey É. Derkachov and Pavel A. Valinevich. SIGMA 21 (2025), 107, 48 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For the noncompact open SL(2, ℂ) spin chain, the eigenfunctions of the special matrix element of the monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter -operators, -operator, and raising operators obtained by reduction from the -operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of the -operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to the reflection of the spin variable → 1 − is established. The Mellin-Barnes representation for eigenfunctions is derived, and equivalence with the initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of the -type Gustafson integral generalized to the complex field.
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| first_indexed | 2026-03-21T12:21:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214186 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:21:47Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. 2026-02-20T07:57:57Z 2025 A-Type Open SL(2, ℂ) Spin Chain. Pavel V. Antonenko, Sergey É. Derkachov and Pavel A. Valinevich. SIGMA 21 (2025), 107, 48 pages 1815-0659 2020 Mathematics Subject Classification: 81R12; 17B80; 33C70 arXiv:2507.09568 https://nasplib.isofts.kiev.ua/handle/123456789/214186 https://doi.org/10.3842/SIGMA.2025.107 For the noncompact open SL(2, ℂ) spin chain, the eigenfunctions of the special matrix element of the monodromy matrix are constructed. The key ingredients of the whole construction are local Yang-Baxter -operators, -operator, and raising operators obtained by reduction from the -operator. The calculation of various scalar products and the proof of orthogonality are based on the properties of the -operator and demonstrate its hidden role. The symmetry of eigenfunctions with respect to the reflection of the spin variable → 1 − is established. The Mellin-Barnes representation for eigenfunctions is derived, and equivalence with the initial coordinate representation is proved. The transformation from one representation to another is grounded on the application of the -type Gustafson integral generalized to the complex field. We are grateful to N. Belousov, S. Khoroshkin, and A. Manashov for fruitful discussions. The work was supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS (S.D. and P.A.) and by the Ministry of Science and Higher Education of the Russian Federation (P.A.), agreement 075-15-2025-344 dated 29/04/2025 for Saint Petersburg Leonhard Euler International Mathematical Institute at PDMI RAS. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A-Type Open SL(2, ℂ) Spin Chain Article published earlier |
| spellingShingle | A-Type Open SL(2, ℂ) Spin Chain Antonenko, Pavel V. Derkachov, Sergey É. Valinevich, Pavel A. |
| title | A-Type Open SL(2, ℂ) Spin Chain |
| title_full | A-Type Open SL(2, ℂ) Spin Chain |
| title_fullStr | A-Type Open SL(2, ℂ) Spin Chain |
| title_full_unstemmed | A-Type Open SL(2, ℂ) Spin Chain |
| title_short | A-Type Open SL(2, ℂ) Spin Chain |
| title_sort | a-type open sl(2, ℂ) spin chain |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214186 |
| work_keys_str_mv | AT antonenkopavelv atypeopensl2cspinchain AT derkachovsergeye atypeopensl2cspinchain AT valinevichpavela atypeopensl2cspinchain |