{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:F5IZ3BUSRV472WPAIQCIVG7HFW","short_pith_number":"pith:F5IZ3BUS","schema_version":"1.0","canonical_sha256":"2f519d86928d79fd59e044048a9be72d853d78d859bb8a3fbd558100c35ae373","source":{"kind":"arxiv","id":"1409.4615","version":3},"attestation_state":"computed","paper":{"title":"Non-Archimedean Whittaker functions as characters: a probabilistic approach to the Shintani-Casselman-Shalika formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT","math.PR"],"primary_cat":"math.RT","authors_text":"Reda Chhaibi","submitted_at":"2014-09-16T13:00:07Z","abstract_excerpt":"For a reductive group $G$ over a non-Archimedean local field (e.g $GL_n( \\mathbb{Q}_p )$ ), Jacquet's Whittaker function is essentially proportional to a character of an irreducible representation of the Langlands dual group $G^\\vee( \\mathbb{C} )$ ( a Schur function if $G = GL_n( \\mathbb{Q}_p )$). We propose a probabilistic approach to this claim, known as the Shintani-Casselman-Shalika formula, when the group $G$ has at least one minuscule cocharacter in the coweight lattice.\n  Our presentation goes along the following lines. Thanks to a minuscule random walk $W^{(z)}$ on the coweight lattice"},"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":"1409.4615","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-09-16T13:00:07Z","cross_cats_sorted":["math.CO","math.NT","math.PR"],"title_canon_sha256":"265304d4e7162d1a9d599c47dd0dead1d6ed0016a75b6c1c7899b9bdde78e72d","abstract_canon_sha256":"b687e367fcbebd89d526a0f082f1cc173b18afcc8ece4eb26e4cae1967dc5e57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:41.458180Z","signature_b64":"09C2FOxZeog1Uw/t6rwCH8FYG9khqAJ2LGVjGI0+i8OF1IJPAzsXR5LTewHVIycc+jlJUWSdpYGYexiKyDUxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f519d86928d79fd59e044048a9be72d853d78d859bb8a3fbd558100c35ae373","last_reissued_at":"2026-05-18T01:11:41.457702Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:41.457702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Archimedean Whittaker functions as characters: a probabilistic approach to the Shintani-Casselman-Shalika formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT","math.PR"],"primary_cat":"math.RT","authors_text":"Reda Chhaibi","submitted_at":"2014-09-16T13:00:07Z","abstract_excerpt":"For a reductive group $G$ over a non-Archimedean local field (e.g $GL_n( \\mathbb{Q}_p )$ ), Jacquet's Whittaker function is essentially proportional to a character of an irreducible representation of the Langlands dual group $G^\\vee( \\mathbb{C} )$ ( a Schur function if $G = GL_n( \\mathbb{Q}_p )$). We propose a probabilistic approach to this claim, known as the Shintani-Casselman-Shalika formula, when the group $G$ has at least one minuscule cocharacter in the coweight lattice.\n  Our presentation goes along the following lines. Thanks to a minuscule random walk $W^{(z)}$ on the coweight lattice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4615","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.4615","created_at":"2026-05-18T01:11:41.457774+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.4615v3","created_at":"2026-05-18T01:11:41.457774+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4615","created_at":"2026-05-18T01:11:41.457774+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5IZ3BUSRV47","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5IZ3BUSRV472WPA","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5IZ3BUS","created_at":"2026-05-18T12:28:28.263976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW","json":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW.json","graph_json":"https://pith.science/api/pith-number/F5IZ3BUSRV472WPAIQCIVG7HFW/graph.json","events_json":"https://pith.science/api/pith-number/F5IZ3BUSRV472WPAIQCIVG7HFW/events.json","paper":"https://pith.science/paper/F5IZ3BUS"},"agent_actions":{"view_html":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW","download_json":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW.json","view_paper":"https://pith.science/paper/F5IZ3BUS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.4615&json=true","fetch_graph":"https://pith.science/api/pith-number/F5IZ3BUSRV472WPAIQCIVG7HFW/graph.json","fetch_events":"https://pith.science/api/pith-number/F5IZ3BUSRV472WPAIQCIVG7HFW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW/action/storage_attestation","attest_author":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW/action/author_attestation","sign_citation":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW/action/citation_signature","submit_replication":"https://pith.science/pith/F5IZ3BUSRV472WPAIQCIVG7HFW/action/replication_record"}},"created_at":"2026-05-18T01:11:41.457774+00:00","updated_at":"2026-05-18T01:11:41.457774+00:00"}