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We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\\mathcal B$ generated by $\\{x_r\\}_{r \\in \\Lambda}$, which generalizes the strong Haagerup inequalities for $\\ast$-free R-diagonal families obtained by Kemp-Speicher \\cite{KeSp}. As an application of our result, we show tha"},"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":"1101.0033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-12-30T02:56:24Z","cross_cats_sorted":[],"title_canon_sha256":"d9a0bfa9022b315e729ad7a00b65115622d66ba07158cb8deaf01823b848d8b3","abstract_canon_sha256":"46d320f74c2d916f24395a97e95063b8a421d727df01d34a4b037088dfcea44a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:16.586008Z","signature_b64":"uDDvkJYdKrxk8/e2+h6MmmsZyiXRP9QM3AsKArpS3kqUvkOdi+07uiyqJ+p8ui3RhshXuKbvC9pOYuLF5sScBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c65ef5dcd2fd6fcd32168f330897011edf278806304269ed4f71c446ffe8b7b","last_reissued_at":"2026-05-18T02:04:16.585399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:16.585399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Symmetries and Strong Haagerup Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael Brannan","submitted_at":"2010-12-30T02:56:24Z","abstract_excerpt":"In this paper, we consider families of operators $\\{x_r\\}_{r \\in \\Lambda}$ in a tracial C$^\\ast$-probability space $(\\mathcal A, \\phi)$, whose joint $\\ast$-distribution is invariant under free complexification and the action of the hyperoctahedral quantum groups $\\{H_n^+\\}_{n \\in \\N}$. We prove a strong form of Haagerup's inequality for the non-self-adjoint operator algebra $\\mathcal B$ generated by $\\{x_r\\}_{r \\in \\Lambda}$, which generalizes the strong Haagerup inequalities for $\\ast$-free R-diagonal families obtained by Kemp-Speicher \\cite{KeSp}. As an application of our result, we show tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0033","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":""},"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":"1101.0033","created_at":"2026-05-18T02:04:16.585502+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.0033v1","created_at":"2026-05-18T02:04:16.585502+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0033","created_at":"2026-05-18T02:04:16.585502+00:00"},{"alias_kind":"pith_short_12","alias_value":"BRS66XONF7LP","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BRS66XONF7LPZUZB","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BRS66XON","created_at":"2026-05-18T12:26:05.355336+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/BRS66XONF7LPZUZBNDZTBCLQCH","json":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH.json","graph_json":"https://pith.science/api/pith-number/BRS66XONF7LPZUZBNDZTBCLQCH/graph.json","events_json":"https://pith.science/api/pith-number/BRS66XONF7LPZUZBNDZTBCLQCH/events.json","paper":"https://pith.science/paper/BRS66XON"},"agent_actions":{"view_html":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH","download_json":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH.json","view_paper":"https://pith.science/paper/BRS66XON","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.0033&json=true","fetch_graph":"https://pith.science/api/pith-number/BRS66XONF7LPZUZBNDZTBCLQCH/graph.json","fetch_events":"https://pith.science/api/pith-number/BRS66XONF7LPZUZBNDZTBCLQCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH/action/storage_attestation","attest_author":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH/action/author_attestation","sign_citation":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH/action/citation_signature","submit_replication":"https://pith.science/pith/BRS66XONF7LPZUZBNDZTBCLQCH/action/replication_record"}},"created_at":"2026-05-18T02:04:16.585502+00:00","updated_at":"2026-05-18T02:04:16.585502+00:00"}