{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T7GA4KII7EQ4WRR3GCAU6JMFT4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5da97f864fbb16d95226a26577fffc66ee6d983cfc12cb731d2d68d2ba77bdca","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-08T08:10:09Z","title_canon_sha256":"1954fbfb8cf767358c40e0f97b8a59a8ee876a879744899988815cd480ed945f"},"schema_version":"1.0","source":{"id":"1103.1456","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1456","created_at":"2026-05-18T03:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1456v2","created_at":"2026-05-18T03:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1456","created_at":"2026-05-18T03:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"T7GA4KII7EQ4","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T7GA4KII7EQ4WRR3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T7GA4KII","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:d921dfd8526d0198f2097e6a1c5f727b523cfb804e0c00bb4bf298533aa64f18","target":"graph","created_at":"2026-05-18T03:18:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we give an explicit combinatorial realization of the crystal B(\\lambda) for an irreducible highest weight U_q(q(n))-module V(\\lambda) in terms of semistandard decomposition tableaux. We present an insertion scheme for semistandard decomposition tableaux and give algorithms of decomposing the tensor product of q(n)-crystals. Consequently, we obtain explicit combinatorial descriptions of the shifted Littlewood-Richardson coefficients.","authors_text":"Dimitar Grantcharov, Ji Hye Jung, Masaki Kashiwara, MyungHo Kim, Seok-Jin Kang","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-08T08:10:09Z","title":"Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1456","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f89798ed200d02f21dc678739ebe11ad9f0e026292264ad323013cfd6ccec536","target":"record","created_at":"2026-05-18T03:18:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5da97f864fbb16d95226a26577fffc66ee6d983cfc12cb731d2d68d2ba77bdca","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-03-08T08:10:09Z","title_canon_sha256":"1954fbfb8cf767358c40e0f97b8a59a8ee876a879744899988815cd480ed945f"},"schema_version":"1.0","source":{"id":"1103.1456","kind":"arxiv","version":2}},"canonical_sha256":"9fcc0e2908f921cb463b30814f25859f11b2ffa60362c8fca92d77dbff42c0be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fcc0e2908f921cb463b30814f25859f11b2ffa60362c8fca92d77dbff42c0be","first_computed_at":"2026-05-18T03:18:32.149769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:32.149769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c93C82pBpH5weEZyuRdiL8kxskeGUhPr3MnXy4uV7IM78JKokH1C807YPxN9kQ4Tp8En9DuAulxBl2zj9n7kAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:32.150521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1456","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f89798ed200d02f21dc678739ebe11ad9f0e026292264ad323013cfd6ccec536","sha256:d921dfd8526d0198f2097e6a1c5f727b523cfb804e0c00bb4bf298533aa64f18"],"state_sha256":"531ed46ebb20406c4264b9ae49b92577d7bfbe2307867d6a9732b39950cda6cf"}