{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VSQ22XRY6M3AVZ72S42D5XAZNE","short_pith_number":"pith:VSQ22XRY","schema_version":"1.0","canonical_sha256":"aca1ad5e38f3360ae7fa97343edc1969252169db82ba5e95b6ea237501a4fd60","source":{"kind":"arxiv","id":"1712.09263","version":1},"attestation_state":"computed","paper":{"title":"The irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(p^f)$ and $\\mathrm{E}_6(p^f)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alessandro Paolini, Kay Magaard, Tung Le","submitted_at":"2017-12-26T13:11:54Z","abstract_excerpt":"We parametrize the set of irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(q)$ and $\\mathrm{E}_6(q)$, for an arbitrary power $q$ of any prime $p$. In particular, we establish that the parametrization is uniform for $p \\ge 3$ in type $\\mathrm{D}_6$ and for $p \\ge 5$ in type $\\mathrm{E}_6$, while the prime $2$ in type $\\mathrm{D}_6$ and the primes $2,$ $3$ in type $\\mathrm{E}_6$ yield character degrees of the form $q^m/p^i$ which force a departure from the generic situations. Also for the first time in our analysis we see a family of irreducible characters "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.09263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-26T13:11:54Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b09aeab840146af4574bf8896a109f7b7ffd7a937393d48a2d4cb16d883e3dde","abstract_canon_sha256":"a3bb4370fc2d062c60fcae8cd03edd7e5ef2896a97c4ad3398f50735c1fe87ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:14.060616Z","signature_b64":"7yKOw8sskNb82wKPaBEaDXOmjedjL2sezllkFL4CCrXfviRZuhNdPAU7u24JqppmsC7cMclIjUN9MOiobxNUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aca1ad5e38f3360ae7fa97343edc1969252169db82ba5e95b6ea237501a4fd60","last_reissued_at":"2026-05-18T00:27:14.060000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:14.060000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(p^f)$ and $\\mathrm{E}_6(p^f)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Alessandro Paolini, Kay Magaard, Tung Le","submitted_at":"2017-12-26T13:11:54Z","abstract_excerpt":"We parametrize the set of irreducible characters of the Sylow $p$-subgroups of the Chevalley groups $\\mathrm{D}_6(q)$ and $\\mathrm{E}_6(q)$, for an arbitrary power $q$ of any prime $p$. In particular, we establish that the parametrization is uniform for $p \\ge 3$ in type $\\mathrm{D}_6$ and for $p \\ge 5$ in type $\\mathrm{E}_6$, while the prime $2$ in type $\\mathrm{D}_6$ and the primes $2,$ $3$ in type $\\mathrm{E}_6$ yield character degrees of the form $q^m/p^i$ which force a departure from the generic situations. Also for the first time in our analysis we see a family of irreducible characters "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09263","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.09263","created_at":"2026-05-18T00:27:14.060089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09263v1","created_at":"2026-05-18T00:27:14.060089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09263","created_at":"2026-05-18T00:27:14.060089+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSQ22XRY6M3A","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSQ22XRY6M3AVZ72","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSQ22XRY","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE","json":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE.json","graph_json":"https://pith.science/api/pith-number/VSQ22XRY6M3AVZ72S42D5XAZNE/graph.json","events_json":"https://pith.science/api/pith-number/VSQ22XRY6M3AVZ72S42D5XAZNE/events.json","paper":"https://pith.science/paper/VSQ22XRY"},"agent_actions":{"view_html":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE","download_json":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE.json","view_paper":"https://pith.science/paper/VSQ22XRY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09263&json=true","fetch_graph":"https://pith.science/api/pith-number/VSQ22XRY6M3AVZ72S42D5XAZNE/graph.json","fetch_events":"https://pith.science/api/pith-number/VSQ22XRY6M3AVZ72S42D5XAZNE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE/action/storage_attestation","attest_author":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE/action/author_attestation","sign_citation":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE/action/citation_signature","submit_replication":"https://pith.science/pith/VSQ22XRY6M3AVZ72S42D5XAZNE/action/replication_record"}},"created_at":"2026-05-18T00:27:14.060089+00:00","updated_at":"2026-05-18T00:27:14.060089+00:00"}