{"paper":{"title":"Interpolating Feigin-Frenkel Duality at the Critical Level to Matrices of Complex Size","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RT"],"primary_cat":"math.QA","authors_text":"Andrew Riesen","submitted_at":"2025-05-15T15:56:49Z","abstract_excerpt":"In this paper, we extend Feigin-Frenkel duality at the critical level to complex rank by identifying two seemingly unrelated constructions in complex rank. On the affine side, we interpolate Molev's construction of higher Segal-Sugawara vectors and thereby describe the centers of universal affine vertex algebras at the critical level in Deligne's interpolating categories. On the $\\mathcal{W}$-side, we construct the classical $\\mathcal{W}$-algebras associated with Feigin's Lie algebras of complex rank $\\mathfrak{gl}_{\\lambda}$ and $\\mathfrak{po}_{\\lambda}$ as Poisson vertex algebras, realizing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10439","kind":"arxiv","version":3},"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/2505.10439/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"}