{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JP3QLQMB66QIPYGPTI2N3YA6B5","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":"0c666e5aeb1b5d0d1031190a27c1705b7d5d193553cbdb8992576a9ec9081e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-29T21:11:48Z","title_canon_sha256":"ab6600b08c533b401f7c996db6bfc0f7c09d925a11a5e27faa0a216df0bd990d"},"schema_version":"1.0","source":{"id":"1312.0021","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0021","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0021v3","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0021","created_at":"2026-05-18T02:40:02Z"},{"alias_kind":"pith_short_12","alias_value":"JP3QLQMB66QI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JP3QLQMB66QIPYGP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JP3QLQMB","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:433435bc39f29bb096bc7d24b48b6b2be495fb636bb56ed800bf010c67bafac5","target":"graph","created_at":"2026-05-18T02:40:02Z","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":"We are interested in the structure of the crystal graph of level $l$ Fock spaces representations of $\\mathcal{U}_q (\\widehat{\\mathfrak{sl}_e})$. Since the work of Shan [26], we know that this graph encodes the modular branching rule for a corresponding cyclotomic rational Cherednik algebra. Besides, it appears to be closely related to the Harish-Chandra branching graph for the appropriate finite unitary group, according to [8]. In this paper, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces. This so-called \"canonical\" crystal isomorphi","authors_text":"Thomas Gerber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-29T21:11:48Z","title":"Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0021","kind":"arxiv","version":3},"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":"sha256:048af0f53dbbf14aa0ec20b61525fef775b3cd1568ab52f604f7d405239278fb","target":"record","created_at":"2026-05-18T02:40:02Z","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":"0c666e5aeb1b5d0d1031190a27c1705b7d5d193553cbdb8992576a9ec9081e2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-11-29T21:11:48Z","title_canon_sha256":"ab6600b08c533b401f7c996db6bfc0f7c09d925a11a5e27faa0a216df0bd990d"},"schema_version":"1.0","source":{"id":"1312.0021","kind":"arxiv","version":3}},"canonical_sha256":"4bf705c181f7a087e0cf9a34dde01e0f4617e2dd048fb11609d2d2e899c1b50b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bf705c181f7a087e0cf9a34dde01e0f4617e2dd048fb11609d2d2e899c1b50b","first_computed_at":"2026-05-18T02:40:02.131515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:02.131515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jIFkooCzVux5TdXS5XStGJS1kOqAtoNmd4S65nRxNK7IWLyRRDO2GQ3+1J2vA5BUf5f0QNP7UYAUDOSEVbimBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:02.132124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0021","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:048af0f53dbbf14aa0ec20b61525fef775b3cd1568ab52f604f7d405239278fb","sha256:433435bc39f29bb096bc7d24b48b6b2be495fb636bb56ed800bf010c67bafac5"],"state_sha256":"ea3df7a104eae233d774dda103b401a0324d5a91a2b219bed9f111fed9a31157"}