{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O5QRF4FOCKGN6UNLKYNUSE4SVE","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":"9f41e04e1cc08bf83309bb732300b8aa0ce49363bd0eb8f7e12f0fd68901de10","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-28T08:35:24Z","title_canon_sha256":"172f7e2313505cc2cef465e47e95c6f12100f76b0e617809f5f283243a3da8e3"},"schema_version":"1.0","source":{"id":"1305.6407","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6407","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6407v1","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6407","created_at":"2026-05-18T03:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"O5QRF4FOCKGN","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O5QRF4FOCKGN6UNL","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O5QRF4FO","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:cbaf5cdedbd9adbb95b71fc4ba4a9d872e0c7831c7e22bb3450a7c57b07327a3","target":"graph","created_at":"2026-05-18T03:24:40Z","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":"As a step to establish the McKay conjecture on character degrees of finite groups, we verify the inductive McKay condition introduced by Isaacs-Malle-Navarro for simple groups of Lie type $A_{n-1}$, split or twisted. Key to the proofs is the study of certain characters of SL$_n(q)$ and SU$_n(q)$ related to generalized Gelfand-Graev representations. As a by-product we can show that a Jordan decomposition for the characters of the latter groups is equivariant under outer automorphisms. Many ideas seem applicable to other Lie types.","authors_text":"Britta Spaeth, Marc Cabanes","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-28T08:35:24Z","title":"Equivariant character correspondences and inductive McKay condition for type A"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6407","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":"sha256:38940cfd1b17e21ee209911f322948b2377e36846b43d61f9018c3a279286cad","target":"record","created_at":"2026-05-18T03:24:40Z","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":"9f41e04e1cc08bf83309bb732300b8aa0ce49363bd0eb8f7e12f0fd68901de10","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-05-28T08:35:24Z","title_canon_sha256":"172f7e2313505cc2cef465e47e95c6f12100f76b0e617809f5f283243a3da8e3"},"schema_version":"1.0","source":{"id":"1305.6407","kind":"arxiv","version":1}},"canonical_sha256":"776112f0ae128cdf51ab561b491392a91a49539cc4dd73f68feae01dc4bafb15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"776112f0ae128cdf51ab561b491392a91a49539cc4dd73f68feae01dc4bafb15","first_computed_at":"2026-05-18T03:24:40.830110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:40.830110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2dS0JZgucU5I5Um9ThJA67BPmU6lsMOL+qH25cZYPDEmPo8f3yK6qQ8Qzr4VC5G7YwlgAQlLAam6c9WsY+hAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:40.830736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6407","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38940cfd1b17e21ee209911f322948b2377e36846b43d61f9018c3a279286cad","sha256:cbaf5cdedbd9adbb95b71fc4ba4a9d872e0c7831c7e22bb3450a7c57b07327a3"],"state_sha256":"fcaa2d3779455356493e37f83677f7383b0246584dc18552ea50c06bbf28287e"}