{"paper":{"title":"Symplectic Differential Reduction Algebras and Generalized Weyl Algebras","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Dwight Anderson Williams II, Jonas T. Hartwig","submitted_at":"2024-03-24T00:08:32Z","abstract_excerpt":"Given a map $\\Xi\\colon U(\\mathfrak{g})\\rightarrow A$ of associative algebras, with $U(\\mathfrak{g})$ the universal enveloping algebra of a (complex) finite-dimensional reductive Lie algebra $\\mathfrak{g}$, the restriction functor from $A$-modules to $U(\\mathfrak{g})$-modules is intimately tied to the representation theory of an $A$-subquotient known as the reduction algebra with respect to $(A,\\mathfrak{g},\\Xi)$. Herlemont and Ogievetsky described differential reduction algebras for the general linear Lie algebra $\\mathfrak{gl}(n)$ as algebras of deformed differential operators. Their map $\\Xi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.15968","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/2403.15968/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"}