{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WRLN6D3G4JCZSGLQDOETM5GKFV","short_pith_number":"pith:WRLN6D3G","schema_version":"1.0","canonical_sha256":"b456df0f66e2459919701b893674ca2d6153b3bb5e86002b22460df64e255e65","source":{"kind":"arxiv","id":"2310.02252","version":1},"attestation_state":"computed","paper":{"title":"Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"quant-ph","authors_text":"Adam Burchardt, Dmitry Grinko, Maris Ozols","submitted_at":"2023-10-03T17:55:10Z","abstract_excerpt":"We study representation theory of the partially transposed permutation matrix algebra, a matrix representation of the diagrammatic walled Brauer algebra. This algebra plays a prominent role in mixed Schur-Weyl duality that appears in various contexts in quantum information. Our main technical result is an explicit formula for the action of the walled Brauer algebra generators in the Gelfand-Tsetlin basis. It generalizes the well-known Gelfand-Tsetlin basis for the symmetric group (also known as Young's orthogonal form or Young-Yamanouchi basis).\n  We provide two applications of our result to q"},"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":"2310.02252","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2023-10-03T17:55:10Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"ace2520ea26f2cb0a322b7248fc9fc4f477643d2e0c3b528d61b985fc5b4057a","abstract_canon_sha256":"d61c32c12ed6129847ae26ed9966b5d520a8b99427de9ce1dc1f580ccc3ebb9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:56:51.914741Z","signature_b64":"t6/r5uS62Ggs2fXmraNSubgZclfg16N04hhupg1mmzULpnZp3kcjpUceBT20E0WGxm8RArLf2JTU61oqugIBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b456df0f66e2459919701b893674ca2d6153b3bb5e86002b22460df64e255e65","last_reissued_at":"2026-07-05T06:56:51.914254Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:56:51.914254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gelfand-Tsetlin basis for partially transposed permutations, with applications to quantum information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"quant-ph","authors_text":"Adam Burchardt, Dmitry Grinko, Maris Ozols","submitted_at":"2023-10-03T17:55:10Z","abstract_excerpt":"We study representation theory of the partially transposed permutation matrix algebra, a matrix representation of the diagrammatic walled Brauer algebra. This algebra plays a prominent role in mixed Schur-Weyl duality that appears in various contexts in quantum information. Our main technical result is an explicit formula for the action of the walled Brauer algebra generators in the Gelfand-Tsetlin basis. It generalizes the well-known Gelfand-Tsetlin basis for the symmetric group (also known as Young's orthogonal form or Young-Yamanouchi basis).\n  We provide two applications of our result to q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.02252","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/2310.02252/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":"2310.02252","created_at":"2026-07-05T06:56:51.914312+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.02252v1","created_at":"2026-07-05T06:56:51.914312+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.02252","created_at":"2026-07-05T06:56:51.914312+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRLN6D3G4JCZ","created_at":"2026-07-05T06:56:51.914312+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRLN6D3G4JCZSGLQ","created_at":"2026-07-05T06:56:51.914312+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRLN6D3G","created_at":"2026-07-05T06:56:51.914312+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":8,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.22343","citing_title":"Probabilistic Storage and Retrieval of Quantum Superchannels for \"Retrospective'' Intervention","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2606.05099","citing_title":"Quantum Time Lower Bounds by Permutation Invariance","ref_index":25,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30281","citing_title":"Quantum Lazy Sampling and Path Recording for Any Group","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2410.16220","citing_title":"Sample Optimal and Memory Efficient Quantum State Tomography","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2409.10393","citing_title":"Multicopy quantum state teleportation with application to storage and retrieval of quantum programs","ref_index":37,"is_internal_anchor":false},{"citing_arxiv_id":"2504.12945","citing_title":"A resource theory of asynchronous quantum information processing","ref_index":52,"is_internal_anchor":false},{"citing_arxiv_id":"2512.21260","citing_title":"Random dilation superchannel","ref_index":49,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04981","citing_title":"Exact identification of unknown unitary processes","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV","json":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV.json","graph_json":"https://pith.science/api/pith-number/WRLN6D3G4JCZSGLQDOETM5GKFV/graph.json","events_json":"https://pith.science/api/pith-number/WRLN6D3G4JCZSGLQDOETM5GKFV/events.json","paper":"https://pith.science/paper/WRLN6D3G"},"agent_actions":{"view_html":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV","download_json":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV.json","view_paper":"https://pith.science/paper/WRLN6D3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.02252&json=true","fetch_graph":"https://pith.science/api/pith-number/WRLN6D3G4JCZSGLQDOETM5GKFV/graph.json","fetch_events":"https://pith.science/api/pith-number/WRLN6D3G4JCZSGLQDOETM5GKFV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV/action/storage_attestation","attest_author":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV/action/author_attestation","sign_citation":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV/action/citation_signature","submit_replication":"https://pith.science/pith/WRLN6D3G4JCZSGLQDOETM5GKFV/action/replication_record"}},"created_at":"2026-07-05T06:56:51.914312+00:00","updated_at":"2026-07-05T06:56:51.914312+00:00"}