{"paper":{"title":"Local Langlands correspondence for the twisted exterior and symmetric square $\\epsilon$-factors of $\\textrm{GL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dongming She","submitted_at":"2019-10-06T21:09:10Z","abstract_excerpt":"Let $F$ be a non-Archimedean local field. Let $\\mathcal{A}_n(F)$ be the set of equivalence classes of irreducible admissible representations of $\\textrm{GL}_n(F)$, and $\\mathcal{G}_n(F)$ be the set of equivalence classes of n-dimensional Frobenius semisimple Weil-Deligne representations of $W'_F$. The local Langlands correspondence(LLC) establishes the reciprocity maps $\\textrm{Rec}_{n,F}: \\mathcal{A}_n(F)\\longrightarrow \\mathcal{G}_n(F)$ , satisfying some nice properties. An important invariant under this correspondence is the L- and $\\epsilon$-factors. This is also expected to be true under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.02525","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/1910.02525/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"}