{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OKMHROBDI2E4MLIXUGC7ZZKCRN","short_pith_number":"pith:OKMHROBD","schema_version":"1.0","canonical_sha256":"729878b8234689c62d17a185fce5428b5843f525dbb90912c30593aaf8412d0c","source":{"kind":"arxiv","id":"1208.5139","version":1},"attestation_state":"computed","paper":{"title":"Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Ji Hye Jung, Seok-Jin Kang","submitted_at":"2012-08-25T15:14:51Z","abstract_excerpt":"We introduce a new family of superalgebras $\\overrightarrow{B}_{r,s}$ for $r, s \\ge 0$ such that $r+s>0$, which we call the walled Brauer superalgebras, and prove the mixed Scur-Weyl-Sergeev duality for queer Lie superalgebras. More precisely, let $\\mathfrak{q}(n)$ be the queer Lie superalgebra, ${\\mathbf V} =\\mathbb{C}^{n|n}$ the natural representation of $\\mathfrak{q}(n)$ and ${\\mathbf W}$ the dual of ${\\mathbf V}$. We prove that, if $n \\ge r+s$, the superalgebra $\\overrightarrow{B}_{r,s}$ is isomorphic to the supercentralizer algebra $_{\\mathfrak{q}(n)}({\\mathbf V}^{\\otimes r} \\otimes {\\mat"},"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":"1208.5139","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-25T15:14:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6c8f52d4370aa3225f84b132c11cb9db43ee8d00785916553bd0d5cd20f77d5a","abstract_canon_sha256":"54aa09df34c6ae7598a56bf3263703771cc584eed5a0fe4901430e759244f3c1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:47:00.291524Z","signature_b64":"kTKx7NdjpYDoCPZHdpBxHppy/PNvgiaDZ4JcmetwH2ziHLC/jldBtM0QcOMHhJnm5042h2yrg7g+1PKYYxOWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"729878b8234689c62d17a185fce5428b5843f525dbb90912c30593aaf8412d0c","last_reissued_at":"2026-05-18T03:47:00.290781Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:47:00.290781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Ji Hye Jung, Seok-Jin Kang","submitted_at":"2012-08-25T15:14:51Z","abstract_excerpt":"We introduce a new family of superalgebras $\\overrightarrow{B}_{r,s}$ for $r, s \\ge 0$ such that $r+s>0$, which we call the walled Brauer superalgebras, and prove the mixed Scur-Weyl-Sergeev duality for queer Lie superalgebras. More precisely, let $\\mathfrak{q}(n)$ be the queer Lie superalgebra, ${\\mathbf V} =\\mathbb{C}^{n|n}$ the natural representation of $\\mathfrak{q}(n)$ and ${\\mathbf W}$ the dual of ${\\mathbf V}$. We prove that, if $n \\ge r+s$, the superalgebra $\\overrightarrow{B}_{r,s}$ is isomorphic to the supercentralizer algebra $_{\\mathfrak{q}(n)}({\\mathbf V}^{\\otimes r} \\otimes {\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5139","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":"1208.5139","created_at":"2026-05-18T03:47:00.290909+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.5139v1","created_at":"2026-05-18T03:47:00.290909+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5139","created_at":"2026-05-18T03:47:00.290909+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKMHROBDI2E4","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKMHROBDI2E4MLIX","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKMHROBD","created_at":"2026-05-18T12:27:16.716162+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/OKMHROBDI2E4MLIXUGC7ZZKCRN","json":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN.json","graph_json":"https://pith.science/api/pith-number/OKMHROBDI2E4MLIXUGC7ZZKCRN/graph.json","events_json":"https://pith.science/api/pith-number/OKMHROBDI2E4MLIXUGC7ZZKCRN/events.json","paper":"https://pith.science/paper/OKMHROBD"},"agent_actions":{"view_html":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN","download_json":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN.json","view_paper":"https://pith.science/paper/OKMHROBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.5139&json=true","fetch_graph":"https://pith.science/api/pith-number/OKMHROBDI2E4MLIXUGC7ZZKCRN/graph.json","fetch_events":"https://pith.science/api/pith-number/OKMHROBDI2E4MLIXUGC7ZZKCRN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN/action/storage_attestation","attest_author":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN/action/author_attestation","sign_citation":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN/action/citation_signature","submit_replication":"https://pith.science/pith/OKMHROBDI2E4MLIXUGC7ZZKCRN/action/replication_record"}},"created_at":"2026-05-18T03:47:00.290909+00:00","updated_at":"2026-05-18T03:47:00.290909+00:00"}