{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OY2TE2NMENZLUFCQWVSSKN7J4A","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":"88e80c5c4c1534514a56a2eb013debe3e011fd52dfe95afe937c54941cba9eb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-16T18:13:23Z","title_canon_sha256":"4e1173a3303fba0eed03ee71ea7f4708777171422d6324f67b33ae85c1f53bb7"},"schema_version":"1.0","source":{"id":"1204.3590","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3590","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3590v3","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3590","created_at":"2026-05-18T03:57:13Z"},{"alias_kind":"pith_short_12","alias_value":"OY2TE2NMENZL","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"OY2TE2NMENZLUFCQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"OY2TE2NM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:3264d8f361222da03b0d630233e4cefa2c6cdc2d61c4c8df3ef4a3510d3669f0","target":"graph","created_at":"2026-05-18T03:57:13Z","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":"Let $W$ be a finite Weyl group and $\\sg$ be a non-trivial graph automorphism of $W$. We show a remarkable relation between the $\\sg$-twisted involution module for $W$ and the Frobenius--Schur indicators of the unipotent characters of a corresponding twisted finite group of Lie type. This extends earlier results of Lusztig-Vogan for the untwisted case and then allows us to state a general result valid for any finite group of Lie type. Inspired by recent work of Marberg, we also formally define Frobenius--Schur indicators for \"unipotent characters\" of twisted dihedral groups.","authors_text":"Gunter Malle, Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-16T18:13:23Z","title":"Frobenius--Schur indicators of unipotent characters and the twisted involution module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3590","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:db51449dd6c99da8b871d0c18b87644c2906fca9c9368556e45e232aaf2a7737","target":"record","created_at":"2026-05-18T03:57:13Z","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":"88e80c5c4c1534514a56a2eb013debe3e011fd52dfe95afe937c54941cba9eb8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-04-16T18:13:23Z","title_canon_sha256":"4e1173a3303fba0eed03ee71ea7f4708777171422d6324f67b33ae85c1f53bb7"},"schema_version":"1.0","source":{"id":"1204.3590","kind":"arxiv","version":3}},"canonical_sha256":"76353269ac2372ba1450b5652537e9e030e2f32551378f35464cb0359ae7261d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76353269ac2372ba1450b5652537e9e030e2f32551378f35464cb0359ae7261d","first_computed_at":"2026-05-18T03:57:13.826657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:13.826657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hWjUM9dJYjMGJL3tLA7+AjYyP640xyL2kNnHy91WND8EKsXONh221z3MkDbbYS0sis5Ygd1OtBqV1gDcSyTYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:13.827204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3590","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db51449dd6c99da8b871d0c18b87644c2906fca9c9368556e45e232aaf2a7737","sha256:3264d8f361222da03b0d630233e4cefa2c6cdc2d61c4c8df3ef4a3510d3669f0"],"state_sha256":"d1ac98007c42ea57832581232e103d83d430683bac7f2c70f8c4d0d03fdf1f3f"}