{"paper":{"title":"The recording tableaux in the quantum Littlewood-Richardson map, the orthogonal transpose symmetry map, and the computation of $\\mathfrak{k}$-highest weight tableaux","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A combinatorial identification proves the surjectivity of the quantum Littlewood-Richardson map on recording tableaux.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Olga Azenhas","submitted_at":"2026-03-17T15:51:49Z","abstract_excerpt":"Recently Watanabe has given an algorithm to compute a bijection, that he calls (quantum) Littlewood-Richardson (LR) map (or quantum LR rule of type AII), between semi-standard Young tableaux of shape a partition with at most $2n$ parts and pairs of tableaux consisting of a symplectic tableau with shape a partition with at most $n$ parts, and a recording tableau of skew-shape given by the two previous shapes. The recording tableaux in that algorithm are shown to be equinumerous to Littlewood-Richardson-Sundaram tableaux whose injectivity is shown combinatorially while the surjectivity is conclu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"one provides a combinatorial proof for the surjectivity of the quantum LR map which in turn exhibits the restriction of the LR orthogonal transpose symmetry map to LR-Sundaram tableaux","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the recording tableaux produced by Watanabe's algorithm are precisely the Littlewood-Richardson-Sundaram tableaux (equinumerosity is asserted but the combinatorial identification must hold for the surjectivity argument to be complete).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A combinatorial proof establishes surjectivity of the quantum LR map and yields an explicit restriction of the orthogonal transpose symmetry map to LR-Sundaram tableaux.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A combinatorial identification proves the surjectivity of the quantum Littlewood-Richardson map on recording tableaux.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"39c79fdcd63c2888c6ff1bf5b506d124d2448ec1ed489bc87107fb1c1b8fc58f"},"source":{"id":"2603.16698","kind":"arxiv","version":3},"verdict":{"id":"d52c2eee-9483-406a-a759-ae62ca7d2a4d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T09:58:13.573602Z","strongest_claim":"one provides a combinatorial proof for the surjectivity of the quantum LR map which in turn exhibits the restriction of the LR orthogonal transpose symmetry map to LR-Sundaram tableaux","one_line_summary":"A combinatorial proof establishes surjectivity of the quantum LR map and yields an explicit restriction of the orthogonal transpose symmetry map to LR-Sundaram tableaux.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the recording tableaux produced by Watanabe's algorithm are precisely the Littlewood-Richardson-Sundaram tableaux (equinumerosity is asserted but the combinatorial identification must hold for the surjectivity argument to be complete).","pith_extraction_headline":"A combinatorial identification proves the surjectivity of the quantum Littlewood-Richardson map on recording tableaux."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.16698/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a852b87710e73a52aa1874aecb2e5251224a96ae119ae96f6d47e0444e0a524d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}