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Let $\\Cal A^0_n(F)$ denote the set of equivalence classes of irreducible cuspidal representations of $\\roman{GL}_n(F)$ and set $\\hat{\\roman{GL}}_F = \\bigcup_{n\\ge1} \\Cal A^0_n(F)$. If $\\sigma\\in \\hat{\\Cal W}_F$, let $\\upr L\\sigma \\in \\hat{\\roman{GL}}_F$ be the cuspidal representation matched with $\\sigma$ by the Langlands Correspondence. If $\\sigma$ is"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1103.5316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-28T10:15:42Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"2115765cfbec8c6627fa9085862d9648507496848ca8168c8adb15d98bdacd6f","abstract_canon_sha256":"1b441c9298894c2716c5aba8f8b70354f176d2cd6bf5f7ec657c237dd070ff26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:58.664479Z","signature_b64":"VthXowaNUhT+Rb0LtLeRKMfAjjRH34QcN/yT9NUMzEuyYIjGStN30DoIsVDOmqG0aFWTn5ldT08jJMT3du3ZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdca79780b3b59028403712c260f3cc5534cc443229f91f765690fbcc5d7f316","last_reissued_at":"2026-05-18T03:10:58.663702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:58.663702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"To an effective local Langlands Corrspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Colin J. Bushnell, Guy Henniart","submitted_at":"2011-03-28T10:15:42Z","abstract_excerpt":"Let $F$ be a non-Archimedean local field. Let $\\Cal W_F$ be the Weil group of $F$ and $\\Cal P_F$ the wild inertia subgroup of $\\scr W_F$. Let $\\hat{\\Cal W}_F$ be the set of equivalence classes of irreducible smooth representations of $\\Cal W_F$. Let $\\Cal A^0_n(F)$ denote the set of equivalence classes of irreducible cuspidal representations of $\\roman{GL}_n(F)$ and set $\\hat{\\roman{GL}}_F = \\bigcup_{n\\ge1} \\Cal A^0_n(F)$. If $\\sigma\\in \\hat{\\Cal W}_F$, let $\\upr L\\sigma \\in \\hat{\\roman{GL}}_F$ be the cuspidal representation matched with $\\sigma$ by the Langlands Correspondence. 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