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We classify irreducible representations of $\\mathcal J(G)$. As a consequence, we prove a conjecture of Bezrukavnikov-Braverman-Kazhdan that the inclusion $\\mathcal H(G)\\subset\\mathcal J(G)$ induces an isomorphism $\\mathcal H(G)/[\\mathcal H(G),\\mathcal H(G)]\\simeq\\mathcal J(G)/[\\mathcal J(G),\\m"},"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":"2407.02752","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2024-07-03T02:02:57Z","cross_cats_sorted":[],"title_canon_sha256":"311b037aedc6944a8b8cb29ba71ede07d6f302c64d5402d9aecb83f06e7bf0c6","abstract_canon_sha256":"20aee7e7c0d2f6f1f92b63c050845a59a9304912daf10677c57473289cd09015"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:39:41.131418Z","signature_b64":"wgRstu3bJPrq3h9L/r+G5YsJwCiztfptQ9G8+DcPCQJOmPBxpCVJuvVIKzY5Xx53S6QQdYizpwhUStmAMB7VDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b87b9548c0408dfd31109b918f8626266bf6a5ff200f89279085af083f7afc","last_reissued_at":"2026-07-05T08:39:41.131025Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:39:41.131025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trace Paley-Wiener theorem for Braverman-Kazhdan's asymptotic Hecke algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kenta Suzuki","submitted_at":"2024-07-03T02:02:57Z","abstract_excerpt":"Let $\\mathbf G$ be a reductive algebraic group over a non-archimedean local field $F$ of characteristic zero and let $G=\\mathbf G(F)$ be the group of $F$-rational points. Let $\\mathcal H(G)$ be the Hecke algebra and let $\\mathcal J(G)$ be the asymptotic Hecke algebra, as defined by Braverman and Kazhdan. We classify irreducible representations of $\\mathcal J(G)$. As a consequence, we prove a conjecture of Bezrukavnikov-Braverman-Kazhdan that the inclusion $\\mathcal H(G)\\subset\\mathcal J(G)$ induces an isomorphism $\\mathcal H(G)/[\\mathcal H(G),\\mathcal H(G)]\\simeq\\mathcal J(G)/[\\mathcal J(G),\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.02752","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/2407.02752/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":"2407.02752","created_at":"2026-07-05T08:39:41.131084+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.02752v1","created_at":"2026-07-05T08:39:41.131084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.02752","created_at":"2026-07-05T08:39:41.131084+00:00"},{"alias_kind":"pith_short_12","alias_value":"I24HXFKIYBAI","created_at":"2026-07-05T08:39:41.131084+00:00"},{"alias_kind":"pith_short_16","alias_value":"I24HXFKIYBAI37JR","created_at":"2026-07-05T08:39:41.131084+00:00"},{"alias_kind":"pith_short_8","alias_value":"I24HXFKI","created_at":"2026-07-05T08:39:41.131084+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21313","citing_title":"On Braverman-Kazhdan's asymptotic Hecke algebra for inner forms of $\\mathrm{GL}_n$","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY","json":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY.json","graph_json":"https://pith.science/api/pith-number/I24HXFKIYBAI37JRCCNZDD4GEY/graph.json","events_json":"https://pith.science/api/pith-number/I24HXFKIYBAI37JRCCNZDD4GEY/events.json","paper":"https://pith.science/paper/I24HXFKI"},"agent_actions":{"view_html":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY","download_json":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY.json","view_paper":"https://pith.science/paper/I24HXFKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.02752&json=true","fetch_graph":"https://pith.science/api/pith-number/I24HXFKIYBAI37JRCCNZDD4GEY/graph.json","fetch_events":"https://pith.science/api/pith-number/I24HXFKIYBAI37JRCCNZDD4GEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY/action/storage_attestation","attest_author":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY/action/author_attestation","sign_citation":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY/action/citation_signature","submit_replication":"https://pith.science/pith/I24HXFKIYBAI37JRCCNZDD4GEY/action/replication_record"}},"created_at":"2026-07-05T08:39:41.131084+00:00","updated_at":"2026-07-05T08:39:41.131084+00:00"}