{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HLNEJUYCAFWVFZCGTKQ3FDO3XR","short_pith_number":"pith:HLNEJUYC","schema_version":"1.0","canonical_sha256":"3ada44d302016d52e4469aa1b28ddbbc58c80ae9565407671e63db2639f26a6b","source":{"kind":"arxiv","id":"2505.17401","version":1},"attestation_state":"computed","paper":{"title":"An involution for Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chuan Qin","submitted_at":"2025-05-23T02:23:09Z","abstract_excerpt":"We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's work. Our results for the finite case focus on the involution theorem for finite Hecke algebras that appear in Howlett-Lehrer's theory, where they proved a version for characters of certain subgroups of a Weyl group. We hope that our results will serve as a stepping stone for the study of involution for an arbitrary Bernstein block in the p-adic reductive gr"},"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":"2505.17401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-05-23T02:23:09Z","cross_cats_sorted":[],"title_canon_sha256":"5ce7108eb15eda3050a8c14d53a12c6ea218fc722996b8edc7beb529efd65984","abstract_canon_sha256":"5c22f9dc5c7852af5d7e62fa4300ed64c42b1ccbc934ba931231cc0c3e783ab8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:08:25.534818Z","signature_b64":"ev2uQbfTObkFHJFbNpNM7Lk91E4bqkH/zo+2btCij7m/FNbfRsxu4c26iL+bY1GoohYG8ky3crptFgQLuz5QCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ada44d302016d52e4469aa1b28ddbbc58c80ae9565407671e63db2639f26a6b","last_reissued_at":"2026-07-05T11:08:25.534274Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:08:25.534274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An involution for Hecke algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chuan Qin","submitted_at":"2025-05-23T02:23:09Z","abstract_excerpt":"We give two generalizations of the Alvis-Curtis duality for Hecke algebras: an unequal parameter version for the affine Hecke algebras, based on S.-I. Kato's work, and a relative version for finite Hecke algebras, based on Howlett-Lehrer's work. Our results for the finite case focus on the involution theorem for finite Hecke algebras that appear in Howlett-Lehrer's theory, where they proved a version for characters of certain subgroups of a Weyl group. We hope that our results will serve as a stepping stone for the study of involution for an arbitrary Bernstein block in the p-adic reductive gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17401","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.17401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.17401","created_at":"2026-07-05T11:08:25.534337+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.17401v1","created_at":"2026-07-05T11:08:25.534337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.17401","created_at":"2026-07-05T11:08:25.534337+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLNEJUYCAFWV","created_at":"2026-07-05T11:08:25.534337+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLNEJUYCAFWVFZCG","created_at":"2026-07-05T11:08:25.534337+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLNEJUYC","created_at":"2026-07-05T11:08:25.534337+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/HLNEJUYCAFWVFZCGTKQ3FDO3XR","json":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR.json","graph_json":"https://pith.science/api/pith-number/HLNEJUYCAFWVFZCGTKQ3FDO3XR/graph.json","events_json":"https://pith.science/api/pith-number/HLNEJUYCAFWVFZCGTKQ3FDO3XR/events.json","paper":"https://pith.science/paper/HLNEJUYC"},"agent_actions":{"view_html":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR","download_json":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR.json","view_paper":"https://pith.science/paper/HLNEJUYC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.17401&json=true","fetch_graph":"https://pith.science/api/pith-number/HLNEJUYCAFWVFZCGTKQ3FDO3XR/graph.json","fetch_events":"https://pith.science/api/pith-number/HLNEJUYCAFWVFZCGTKQ3FDO3XR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR/action/storage_attestation","attest_author":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR/action/author_attestation","sign_citation":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR/action/citation_signature","submit_replication":"https://pith.science/pith/HLNEJUYCAFWVFZCGTKQ3FDO3XR/action/replication_record"}},"created_at":"2026-07-05T11:08:25.534337+00:00","updated_at":"2026-07-05T11:08:25.534337+00:00"}