{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2K2SA5NX536ENOODZV7J7CCBQD","short_pith_number":"pith:2K2SA5NX","schema_version":"1.0","canonical_sha256":"d2b52075b7eefc46b9c3cd7e9f884180d4a46d4440a06ddfb37af2dfcc1b2b19","source":{"kind":"arxiv","id":"1704.03019","version":5},"attestation_state":"computed","paper":{"title":"Remarks on the asymptotic Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Braverman, David Kazhdan","submitted_at":"2017-04-10T19:11:47Z","abstract_excerpt":"Let $G$ be a split reductive $p$-adic group. Let ${\\mathcal H}(G)$ be its Hecke algebra and let ${\\mathcal C}(G)\\supset {\\mathcal H}(G)$ be the Harish-Chandra Schwartz algebra. The purpose of this note is to give a spectral interpretation of Lusztig's asymptotic Hecke algebra $J$ (which contains the Iwahori part of ${\\mathcal H}(G)$ as a subalgebra), which shows that $J$ is a subalgebra of ${\\mathcal C} (G)$. This spectral description also allows to define a version of $J$ beyond the Iwahori component - i.e. we define certain subalgebra ${\\mathcal J}(G)$ of ${\\mathcal C}(G)$ which contains ${\\"},"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":"1704.03019","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-10T19:11:47Z","cross_cats_sorted":[],"title_canon_sha256":"4bb0774fd1c38d267d8f52788c5e9cc7b776f970efee99bd3afc38f9616a84bd","abstract_canon_sha256":"77c76cbacdf5aeb7fc54bbaea3775d42bd1cebfd14e2f05514c9bb53086c930a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:22.606096Z","signature_b64":"b8mfYV0mseC/qyyBUE/5zgrBhBDf9Kt9au2Y4sx5mHWilOb8gW0V4nMOM0H5M30EnoXkKePC60BFjdSV1ErDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2b52075b7eefc46b9c3cd7e9f884180d4a46d4440a06ddfb37af2dfcc1b2b19","last_reissued_at":"2026-05-18T00:02:22.605511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:22.605511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks on the asymptotic Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Braverman, David Kazhdan","submitted_at":"2017-04-10T19:11:47Z","abstract_excerpt":"Let $G$ be a split reductive $p$-adic group. Let ${\\mathcal H}(G)$ be its Hecke algebra and let ${\\mathcal C}(G)\\supset {\\mathcal H}(G)$ be the Harish-Chandra Schwartz algebra. The purpose of this note is to give a spectral interpretation of Lusztig's asymptotic Hecke algebra $J$ (which contains the Iwahori part of ${\\mathcal H}(G)$ as a subalgebra), which shows that $J$ is a subalgebra of ${\\mathcal C} (G)$. This spectral description also allows to define a version of $J$ beyond the Iwahori component - i.e. we define certain subalgebra ${\\mathcal J}(G)$ of ${\\mathcal C}(G)$ which contains ${\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03019","kind":"arxiv","version":5},"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":"1704.03019","created_at":"2026-05-18T00:02:22.605589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.03019v5","created_at":"2026-05-18T00:02:22.605589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.03019","created_at":"2026-05-18T00:02:22.605589+00:00"},{"alias_kind":"pith_short_12","alias_value":"2K2SA5NX536E","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2K2SA5NX536ENOOD","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2K2SA5NX","created_at":"2026-05-18T12:30:55.937587+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/2K2SA5NX536ENOODZV7J7CCBQD","json":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD.json","graph_json":"https://pith.science/api/pith-number/2K2SA5NX536ENOODZV7J7CCBQD/graph.json","events_json":"https://pith.science/api/pith-number/2K2SA5NX536ENOODZV7J7CCBQD/events.json","paper":"https://pith.science/paper/2K2SA5NX"},"agent_actions":{"view_html":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD","download_json":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD.json","view_paper":"https://pith.science/paper/2K2SA5NX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.03019&json=true","fetch_graph":"https://pith.science/api/pith-number/2K2SA5NX536ENOODZV7J7CCBQD/graph.json","fetch_events":"https://pith.science/api/pith-number/2K2SA5NX536ENOODZV7J7CCBQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD/action/storage_attestation","attest_author":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD/action/author_attestation","sign_citation":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD/action/citation_signature","submit_replication":"https://pith.science/pith/2K2SA5NX536ENOODZV7J7CCBQD/action/replication_record"}},"created_at":"2026-05-18T00:02:22.605589+00:00","updated_at":"2026-05-18T00:02:22.605589+00:00"}