{"paper":{"title":"Quantum $\\mathfrak{gl}$-weight system and its average values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Mikhail Zaitsev","submitted_at":"2025-06-21T12:54:09Z","abstract_excerpt":"We present a proof of a recent conjecture due to M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro, which describes the average value of the universal $\\mathfrak{gl}$-weight system on permutations. The proof uses a quantum analogue of the $\\mathfrak{gl}$-weight system on Hecke algebras of type $A$, which leads to a one-parameter deformation of the average value of the universal ${\\mathfrak{gl}}$-weight system. We show that the average value of the quantum weight system is a linear combination of one-part Schur functions, with coefficients being $q$-analogues of Bernoulli polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17706","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.17706/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"}