{"paper":{"title":"Epsilon factors as algebraic characters on the smooth dual of $\\mathrm{GL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Roger Plymen","submitted_at":"2016-06-05T11:50:54Z","abstract_excerpt":"Let $K$ be a non-archimedean local field and let $G = \\mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this complex structure. The epsilon factors, up to a constant term, factor as invariant characters through the corresponding complex tori. For the arithmetically unramified smooth dual of $\\mathrm{GL}_n$, we provide explicit formulas for the invariant characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01497","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":""},"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"}