{"paper":{"title":"Athinization of irreducible $\\widehat{\\mathfrak{gl}}_n$-modules with dominant highest weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Aleksandr Trufanov, Evgeny Mukhin, Leonid Rybnikov, Mikhail Bershtein","submitted_at":"2026-07-08T17:09:36Z","abstract_excerpt":"We study the Gelfand-Tsetlin realization of generic Verma modules for the affine Lie algebra $\\widehat{\\mathfrak{gl}}_n$ by viewing them as thin modules over the affine Yangian $Y(\\widehat{\\mathfrak{sl}}_n)$. By results of arXiv:0812.4656, these modules admit a basis indexed by periodic Gelfand-Tsetlin patterns with explicit formulas for the Yangian action, and we identify them with the evaluation modules introduced by Kodera arXiv:1806.09884.\n  Our main result describes the specialization from generic highest weights to dominant highest weights (not necessarily integral). We call the resultin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07653","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/2607.07653/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"}