{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2COBY7XT3TRO73Z527PE7626EN","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":"fcf38acedda6b2aac41da883d77b155a5f50d21ce32feacee7ff12d6ae39d5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-10T18:48:58Z","title_canon_sha256":"21a60fc4bd9b8efd7a6469450d440c7678a6c10eb43bcf9585326113013e3ea4"},"schema_version":"1.0","source":{"id":"1509.03269","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03269","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03269v1","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03269","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"2COBY7XT3TRO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2COBY7XT3TRO73Z5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2COBY7XT","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:fadf5626566874adc9ca5c3169d2e34295423dc7f039de56f96d45a2e45dae36","target":"graph","created_at":"2026-05-18T01:33:24Z","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":"Using Harish-Chandra induction and restriction, we construct a categorical action of a Kac-Moody algebra on the category of unipotent representations of finite unitary groups in non-defining characteristic. We show that the decategorified representation is naturally isomorphic to a direct sum of level 2 Fock spaces. From our construction we deduce that the Harish-Chandra branching graph coincide with the crystal graph of these Fock spaces, solving a recent conjecture of Gerber-Hiss-Jacon. We also obtain derived equivalences between blocks, yielding Brou\\'e's abelian defect groups conjecture fo","authors_text":"Eric Vasserot, Michela Varagnolo, Olivier Dudas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-10T18:48:58Z","title":"Categorical actions on unipotent representations I. Finite unitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03269","kind":"arxiv","version":1},"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:f73ce2ec50de758de5af1bd596e1a88e75b7a7b2aa7e66056ee13bf2fce24608","target":"record","created_at":"2026-05-18T01:33:24Z","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":"fcf38acedda6b2aac41da883d77b155a5f50d21ce32feacee7ff12d6ae39d5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-09-10T18:48:58Z","title_canon_sha256":"21a60fc4bd9b8efd7a6469450d440c7678a6c10eb43bcf9585326113013e3ea4"},"schema_version":"1.0","source":{"id":"1509.03269","kind":"arxiv","version":1}},"canonical_sha256":"d09c1c7ef3dce2efef3dd7de4ffb5e2347b341d7b175a2833623a9f5114289b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d09c1c7ef3dce2efef3dd7de4ffb5e2347b341d7b175a2833623a9f5114289b6","first_computed_at":"2026-05-18T01:33:24.883959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:24.883959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKsXU2yfT0uF52by3xhlGYh6CJiV8F9Oj0bySE9ebUz8OFvAfvcluaLtqi2gXqhklAbIMBUf7rGJ1y1NYTtnDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:24.884591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03269","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f73ce2ec50de758de5af1bd596e1a88e75b7a7b2aa7e66056ee13bf2fce24608","sha256:fadf5626566874adc9ca5c3169d2e34295423dc7f039de56f96d45a2e45dae36"],"state_sha256":"77356a7ae8da45e21e987348a06ce3003c3c852d28951ef34d1df088aa162cd8"}