{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:SY5XW3ZHIPERWMS5OLY44D5CP3","short_pith_number":"pith:SY5XW3ZH","schema_version":"1.0","canonical_sha256":"963b7b6f2743c91b325d72f1ce0fa27eeb97c5cc5d2a9a8b066996e3453d83bb","source":{"kind":"arxiv","id":"0909.1227","version":2},"attestation_state":"computed","paper":{"title":"Analytic R-groups of affine Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eric Opdam, Patrick Delorme","submitted_at":"2009-09-07T12:03:02Z","abstract_excerpt":"We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex group algebra of the $R$-group, twisted by a certain 2-cocycle $\\gamma$. For classical Hecke algebras we prove that $\\gamma$ is always trivial."},"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":"0909.1227","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-09-07T12:03:02Z","cross_cats_sorted":[],"title_canon_sha256":"86d0311345393cd798c62148284bc27a62c55f2dcd2de9c85353390e7abc4d29","abstract_canon_sha256":"0ddb61f179e0d1260b980a119c47054d6f14943582022df13782f49ca2040073"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:36.802236Z","signature_b64":"cnNsKbdRWa+633iZ+dt1xtg0M6JODjOR2efXsx+fyk1j0ENEV4Jur7Mh1BTC9+P4S+6NO2iAdapCVgJawxcDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"963b7b6f2743c91b325d72f1ce0fa27eeb97c5cc5d2a9a8b066996e3453d83bb","last_reissued_at":"2026-05-18T04:41:36.801850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:36.801850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic R-groups of affine Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eric Opdam, Patrick Delorme","submitted_at":"2009-09-07T12:03:02Z","abstract_excerpt":"We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex group algebra of the $R$-group, twisted by a certain 2-cocycle $\\gamma$. For classical Hecke algebras we prove that $\\gamma$ is always trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1227","kind":"arxiv","version":2},"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":"0909.1227","created_at":"2026-05-18T04:41:36.801906+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.1227v2","created_at":"2026-05-18T04:41:36.801906+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1227","created_at":"2026-05-18T04:41:36.801906+00:00"},{"alias_kind":"pith_short_12","alias_value":"SY5XW3ZHIPER","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"SY5XW3ZHIPERWMS5","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"SY5XW3ZH","created_at":"2026-05-18T12:26:01.383474+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/SY5XW3ZHIPERWMS5OLY44D5CP3","json":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3.json","graph_json":"https://pith.science/api/pith-number/SY5XW3ZHIPERWMS5OLY44D5CP3/graph.json","events_json":"https://pith.science/api/pith-number/SY5XW3ZHIPERWMS5OLY44D5CP3/events.json","paper":"https://pith.science/paper/SY5XW3ZH"},"agent_actions":{"view_html":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3","download_json":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3.json","view_paper":"https://pith.science/paper/SY5XW3ZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.1227&json=true","fetch_graph":"https://pith.science/api/pith-number/SY5XW3ZHIPERWMS5OLY44D5CP3/graph.json","fetch_events":"https://pith.science/api/pith-number/SY5XW3ZHIPERWMS5OLY44D5CP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3/action/storage_attestation","attest_author":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3/action/author_attestation","sign_citation":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3/action/citation_signature","submit_replication":"https://pith.science/pith/SY5XW3ZHIPERWMS5OLY44D5CP3/action/replication_record"}},"created_at":"2026-05-18T04:41:36.801906+00:00","updated_at":"2026-05-18T04:41:36.801906+00:00"}