{"paper":{"title":"Non-combinatorial involutive braidings: the quantum algebra $\\mathfrak{gl}_{k,m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Involutive non-combinatorial solutions of the braid equation define the gl_{k,m} Yangian as a subalgebra whose highest-weight modules diagonalize quantum spin-chain Hamiltonians.","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Anastasia Doikou","submitted_at":"2026-05-15T16:05:32Z","abstract_excerpt":"We investigate involutive, non-combinatorial solutions of the braid equation viewed as special deformations of the permutation map. By employing these solutions, we identify the associated quantum algebra, which we introduce as the $\\mathfrak{gl}_{k,m}$ Yangian. The algebra $\\mathfrak{gl}_{k,m}$ is also recognized as a subalgebra of the Yangian. Furthermore, we construct specific highest-weight modules of $\\mathfrak{gl}_{k,m},$ which simultaneously yield the eigenstates of certain quantum spin-chain-like Hamiltonians. In the special case of the algebra $\\mathfrak{gl}_{1,1}$ the spin chain Hami"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By employing these solutions, we identify the associated quantum algebra, which we introduce as the gl_{k,m} Yangian. The algebra gl_{k,m} is also recognized as a subalgebra of the Yangian. Furthermore, we construct specific highest-weight modules of gl_{k,m}, which simultaneously yield the eigenstates of certain quantum spin-chain-like Hamiltonians.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The involutive non-combinatorial solutions of the braid equation can be viewed as special deformations of the permutation map in a way that consistently produces a well-defined quantum algebra structure and its highest-weight modules without internal contradictions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Defines the gl_{k,m} Yangian as a subalgebra of the Yangian from non-combinatorial braid solutions and constructs its highest-weight modules as eigenstates of associated spin-chain Hamiltonians, reducing to a Heisenberg XX variant for gl_{1,1}.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Involutive non-combinatorial solutions of the braid equation define the gl_{k,m} Yangian as a subalgebra whose highest-weight modules diagonalize quantum spin-chain Hamiltonians.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5c463effe64912c8914eed5a8fba19e3055002bfd325c72d01991c64aeb21828"},"source":{"id":"2605.16121","kind":"arxiv","version":1},"verdict":{"id":"dc7d4f64-3fd1-4f21-a1c6-2975841ea020","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:07:38.205071Z","strongest_claim":"By employing these solutions, we identify the associated quantum algebra, which we introduce as the gl_{k,m} Yangian. The algebra gl_{k,m} is also recognized as a subalgebra of the Yangian. Furthermore, we construct specific highest-weight modules of gl_{k,m}, which simultaneously yield the eigenstates of certain quantum spin-chain-like Hamiltonians.","one_line_summary":"Defines the gl_{k,m} Yangian as a subalgebra of the Yangian from non-combinatorial braid solutions and constructs its highest-weight modules as eigenstates of associated spin-chain Hamiltonians, reducing to a Heisenberg XX variant for gl_{1,1}.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The involutive non-combinatorial solutions of the braid equation can be viewed as special deformations of the permutation map in a way that consistently produces a well-defined quantum algebra structure and its highest-weight modules without internal contradictions.","pith_extraction_headline":"Involutive non-combinatorial solutions of the braid equation define the gl_{k,m} Yangian as a subalgebra whose highest-weight modules diagonalize quantum spin-chain Hamiltonians."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16121/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:33.848228Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T17:31:18.411504Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:16:19.281324Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.473160Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"72b179d94bdd70a4caff362b6e9c3b74699dcbf21643d7e6dd8e7a42bad87fc1"},"references":{"count":27,"sample":[{"doi":"","year":1982,"title":"Baxter,Exactly solved models in statistical mechanics, Academic Press (1982)","work_id":"d180bb86-bd77-41eb-ab0f-6a20a3df56dd","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1983,"title":"A. Berele and A. Regev,Hook Young diagrams, combinatorics and representations of Lie superalgebras, Bull. Amer. Math. Soc. (N.S.), 8(2) (1983) 337–339","work_id":"dc1450ed-3952-4bde-a43b-a222ace0c7a1","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"N. Cramp´ e, R. Nepomechie, L. Vinet and N. Zare Harofteh,su(2)symmetry of XX spin chains, Math. Phys. Analysis and Geometry (2026) 29:3","work_id":"b1d09f7f-29e3-48b6-9c92-40860fa2ced1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"A. Doikou and P.P. Martin,Hecke algebraic approach to the reflection equation for spin chains, J. Phys. 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