{"paper":{"title":"Double Yangian and reflection algebras of the Lie superalgebra $\\mathfrak{gl}_{M|N}$, II: Quantum currents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Lucia Bagnoli, Slaven Ko\\v{z}i\\'{c}","submitted_at":"2026-08-12T15:25:37Z","abstract_excerpt":"In this paper, we continue our research on the double Yangian and reflection algebras of the Lie superalgebra $\\mathfrak{gl}_{M|N}$. We construct families of central elements in the double Yangian for $\\mathfrak{gl}_{M|N}$ at the critical level. Next, extending the Etingof-Kazhdan construction, we introduce the structure of $h$-adic quantum vertex superalgebra on the vacuum module $V^c(\\mathfrak{gl}_{M|N})$ over the double Yangian of level $c\\in\\mathbb{C}$. Finally, we show that restricted modules over the reflection algebra of $\\mathfrak{gl}_{M|N}$ are naturally equipped with the structure of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12162","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/2608.12162/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"}