{"paper":{"title":"Temperley-Lieb Immanants of Ribbon Decomposition Matrices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Temperley-Lieb immanants evaluate to Schur-positive polynomials on ribbon decomposition matrices.","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Pavlo Pylyavskyy, Son Nguyen","submitted_at":"2026-05-13T01:51:55Z","abstract_excerpt":"Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The ribbon decomposition matrices and the Temperley-Lieb immanants satisfy the combinatorial and algebraic properties needed for the positivity evaluation to hold as stated, relying on definitions and prior results such as Haiman's for the special case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Temperley-Lieb immanants are Schur-positive on ribbon decomposition matrices, extending known Jacobi-Trudi cases, with a conjecture for the full dual canonical basis.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Temperley-Lieb immanants evaluate to Schur-positive polynomials on ribbon decomposition matrices.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2edc0bda9330735f4d7c9ea95c65556e9d90724bb043e0abd97e4561dead345e"},"source":{"id":"2605.12880","kind":"arxiv","version":1},"verdict":{"id":"cf6b6f29-9ad2-40c9-85e5-f5a4af5dd1ca","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:36:11.571797Z","strongest_claim":"We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices.","one_line_summary":"Temperley-Lieb immanants are Schur-positive on ribbon decomposition matrices, extending known Jacobi-Trudi cases, with a conjecture for the full dual canonical basis.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The ribbon decomposition matrices and the Temperley-Lieb immanants satisfy the combinatorial and algebraic properties needed for the positivity evaluation to hold as stated, relying on definitions and prior results such as Haiman's for the special case.","pith_extraction_headline":"Temperley-Lieb immanants evaluate to Schur-positive polynomials on ribbon decomposition matrices."},"references":{"count":63,"sample":[{"doi":"10.1016/0196-6774(84)90002-6","year":1984,"title":"Remmel, J. 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