{"paper":{"title":"Local Langlands correspondence for $GL_n$ and the exterior and symmetric square $\\varepsilon$--factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Freydoon Shahidi, James W. Cogdell, Tung-Lin Tsai","submitted_at":"2014-12-03T19:25:16Z","abstract_excerpt":"Let $F$ be a $p$--adic field, i.e., a finite extension of $\\mathbb Q_p$ for some prime $p$. The local Langlands correspondence attaches to each continuous $n$--dimensional $\\Phi$-semisimple representation $\\rho$ of $W'_F$, the Weil--Deligne group for $\\bar F/F$, an irreducible admissible representation $\\pi(\\rho)$ of $GL_n(F)$ such that, among other things, the local $L$- and $\\varepsilon$-factors of pairs are preserved. This correspondence should be robust and preserve various parallel operations on the arithmetic and analytic sides, such as taking the exterior square or symmetric square. In "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1448","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":""},"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"}