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We describe in an explicit way (1) the action of the Hecke operators on a basis of the cusp forms, which consists of $q$ elements; and (2) the correspondence that assigns to a pure irreducible rank 2 local system $E$ on $\\mathbf{P}^1 \\setminus D$ with unipotent monodromy its Hecke eigensheaf on the moduli space of rank 2 parabolic vector bu"},"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":"1906.03240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-07T17:01:36Z","cross_cats_sorted":[],"title_canon_sha256":"94d28e37b89b4d21ca713ebdbb44f3aba99b251221613a67960f650a0b724d42","abstract_canon_sha256":"162f4cb447a96951118c89076e5f56e11a5e5f01b33e1cb40efe69597dcc9d2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:54.614385Z","signature_b64":"vjRWbJfhocIQ+oC4x8WJhgWAfNM17fEfg0BRNby/f6peem2SR/KHcL27ca95XISQaqoczBTYe4bfHX5TtzoRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e09683319e778f5eedff14e4dfa12efe77512ce5773f917721b6e424393e784e","last_reissued_at":"2026-05-17T23:43:54.613781Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:54.613781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An explicit geometric Langlands correspondence for the projective line minus four points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Niels uit de Bos","submitted_at":"2019-06-07T17:01:36Z","abstract_excerpt":"This article deals with the tamely ramified geometric Langlands correspondence for GL_2 on $\\mathbf{P}_{\\mathbf{F}_q}^1$, where $q$ is a prime power, with tame ramification at four distinct points $D = \\{\\infty, 0,1, t\\} \\subset \\mathbf{P}^1(\\mathbf{F}_q)$. 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