{"paper":{"title":"Neveu--Schwarz Irregular Vertex Operators, Decomposition Theorems, and Bilinear Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hajime Nagoya","submitted_at":"2026-08-13T02:14:52Z","abstract_excerpt":"We construct rank-zero irregular vertex operators for the Neveu--Schwarz algebra as linear maps between irregular Verma modules of the same rank satisfying the usual superconformal commutation relations and an irregular asymptotic condition. Under the nondegeneracy assumption $\\Lambda_{2p}\\neq0$, we prove their existence and uniqueness. We then extend the decomposition theorem for the Neveu--Schwarz algebra to the irregular setting: the tensor product of the free-fermion Fock module with a rank-$p$ Neveu--Schwarz irregular Verma module decomposes into an infinite direct sum of tensor products "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.12727","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/2608.12727/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"}