{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KALCXBJPV3BAOOULK4TNK6ZLT5","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":"d605bce3a83df4dfe838dd21060b08b83bb8dec8f7cb0a081c8baf9256a65fdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-23T13:45:34Z","title_canon_sha256":"ea35f8d83566a71e7c4145d6db7e33b12429e6ca656c270f301e1f4c65dc2ef3"},"schema_version":"1.0","source":{"id":"1603.07179","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07179","created_at":"2026-05-18T01:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07179v4","created_at":"2026-05-18T01:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07179","created_at":"2026-05-18T01:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"KALCXBJPV3BA","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KALCXBJPV3BAOOUL","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KALCXBJP","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:c89e1abd7fcbebc05f67a41eac10407eed639bcbca49b39f02fe36c8e24c5842","target":"graph","created_at":"2026-05-18T01:03:50Z","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":"The traditional construction of Chevalley groups relies on the choice of certain signs for a Chevalley basis of the underlying Lie algebra~$\\mathfrak{g}$. Recently, Lusztig simplified this construction for groups of adjoint type by using the \"canonical basis\" of the adjoint representation of~$\\mathfrak{g}$, in particular, no choices of signs are required. The purpose of this note is to extend this to Chevalley groups which are not necessarily of adjoint type, using Jantzen's explicit models of the minuscule highest weight representations of~$\\mathfrak{g}$.","authors_text":"Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-23T13:45:34Z","title":"Minuscule weights and Chevalley groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07179","kind":"arxiv","version":4},"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":"sha256:678ebbc6b6c242297fd37c44203d7bc99937f8f505c269e9079fdde32d741e1a","target":"record","created_at":"2026-05-18T01:03:50Z","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":"d605bce3a83df4dfe838dd21060b08b83bb8dec8f7cb0a081c8baf9256a65fdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-23T13:45:34Z","title_canon_sha256":"ea35f8d83566a71e7c4145d6db7e33b12429e6ca656c270f301e1f4c65dc2ef3"},"schema_version":"1.0","source":{"id":"1603.07179","kind":"arxiv","version":4}},"canonical_sha256":"50162b852faec2073a8b5726d57b2b9f4b31b4fc44ddf579ec8e121b160f56cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50162b852faec2073a8b5726d57b2b9f4b31b4fc44ddf579ec8e121b160f56cf","first_computed_at":"2026-05-18T01:03:50.260373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:50.260373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xWuJTohq9cvAU+I4/h+czGrCfPsWEiUfjod47YY7Dm1Xle7eiNJW8H8YApklA9Izpkbo1KNCjgC7Q5lfjztDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:50.260917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07179","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:678ebbc6b6c242297fd37c44203d7bc99937f8f505c269e9079fdde32d741e1a","sha256:c89e1abd7fcbebc05f67a41eac10407eed639bcbca49b39f02fe36c8e24c5842"],"state_sha256":"4ee2f6aebf8e458b69bee4cfe123d119853b45c68fe6efdf0668e4ac0a02aae4"}