{"paper":{"title":"Monoidal Jantzen filtrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A monoidal Jantzen filtration deforms the Grothendieck ring multiplication into an associative quantization that matches the geometric version for simply-laced quantum loop algebras.","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"David Hernandez, Ryo Fujita","submitted_at":"2024-02-21T05:53:28Z","abstract_excerpt":"We introduce a monoidal analogue of Jantzen filtrations in the framework of monoidal abelian categories with generic braidings. It leads to a deformation of the multiplication of the Grothendieck ring. We conjecture, and we prove in many remarkable situations, that this deformation is associative so that our construction yields a quantization of the Grothendieck ring as well as analogs of Kazhdan-Lusztig polynomials. As a first main example, for finite-dimensional representations of simply-laced quantum loop algebras, we prove the associativity and we establish that the resulting quantization "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The monoidal Jantzen filtration induces a deformation of the multiplication on the Grothendieck ring that is associative for finite-dimensional representations of simply-laced quantum loop algebras, and the resulting quantization coincides with the quantum Grothendieck ring of Nakajima and Varagnolo-Vasserot.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The monoidal abelian category admits a generic braiding and satisfies the technical conditions needed for the Jantzen filtration to be well-defined and to induce a deformation whose associativity can be checked via explicit computations in the cited representation categories.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Monoidal Jantzen filtrations induce an associative deformation of Grothendieck ring multiplication that quantizes the ring and recovers known quantum versions in representation categories of quantum loop algebras and quiver Hecke algebras.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A monoidal Jantzen filtration deforms the Grothendieck ring multiplication into an associative quantization that matches the geometric version for simply-laced quantum loop algebras.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6ec4fb92f684368364cfaf3c5d0f676d0a6b57ba3132d6005ef207af8a794ff9"},"source":{"id":"2402.13544","kind":"arxiv","version":5},"verdict":{"id":"a2636002-1048-4283-8470-f48f806ebba5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T04:19:08.073140Z","strongest_claim":"The monoidal Jantzen filtration induces a deformation of the multiplication on the Grothendieck ring that is associative for finite-dimensional representations of simply-laced quantum loop algebras, and the resulting quantization coincides with the quantum Grothendieck ring of Nakajima and Varagnolo-Vasserot.","one_line_summary":"Monoidal Jantzen filtrations induce an associative deformation of Grothendieck ring multiplication that quantizes the ring and recovers known quantum versions in representation categories of quantum loop algebras and quiver Hecke algebras.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The monoidal abelian category admits a generic braiding and satisfies the technical conditions needed for the Jantzen filtration to be well-defined and to induce a deformation whose associativity can be checked via explicit computations in the cited representation categories.","pith_extraction_headline":"A monoidal Jantzen filtration deforms the Grothendieck ring multiplication into an associative quantization that matches the geometric version for simply-laced quantum loop algebras."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.13544/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}