{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:45:42Z","timestamp":1760237142323,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,1]],"date-time":"2020-03-01T00:00:00Z","timestamp":1583020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004564","name":"Ministarstvo Prosvete, Nauke i Tehnolo\u0161kog Razvoja","doi-asserted-by":"publisher","award":["ON 171031"],"award-info":[{"award-number":["ON 171031"]}],"id":[{"id":"10.13039\/501100004564","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin\u2019s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way\u2014by obtaining Bethe equations and the spectrum of the generating function\u2014we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.<\/jats:p>","DOI":"10.3390\/sym12030352","type":"journal-article","created":{"date-parts":[[2020,3,2]],"date-time":"2020-03-02T07:50:53Z","timestamp":1583135453000},"page":"352","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Algebraic Bethe Ansatz for the Trigonometric s\u2113(2) Gaudin Model with Triangular Boundary"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1054-3063","authenticated-orcid":false,"given":"Nenad","family":"Manojlovi\u0107","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, F. C. T., Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1119-730X","authenticated-orcid":false,"given":"Igor","family":"Salom","sequence":"additional","affiliation":[{"name":"Institute of Physics, University of Belgrade, P.O. Box 57, 11080 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1051\/jphys:0197600370100108700","article-title":"Diagonalisation d\u2019une classe d\u2019hamiltoniens de spin","volume":"37","author":"Gaudin","year":"1976","journal-title":"J. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.nuclphysb.2004.11.008","article-title":"Exactly-solvable models derived from a generalized Gaudin algebra","volume":"707","author":"Ortiz","year":"2005","journal-title":"Nuclear Phys. 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