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We construct a canonical correspondence between irreducible characters of degree coprime to $3$ of $G$ and those of $N_{G}(P)$, where $P$ is a Sylow $3$-subgroup of $G$. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that fields of values of character correspondents are the same."},"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":"1704.07579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-04-25T08:22:37Z","cross_cats_sorted":[],"title_canon_sha256":"ca44949549d7c3fdf5d52cbbf72ceb5432b6bd49b358951b8d708529589b81ee","abstract_canon_sha256":"a0337319b59f95b3b6b87aad30898e07005bb90fa8c95a7d3fb9987685e25a5e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:37.613823Z","signature_b64":"dbF1uWWhBohzamlBGW/0EBBEuSsfRvyJMhL+4p8ICEdPGZjy58THjyh6aAHkf0r26YzeaHXjgsi1IPj9QOPbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19da737795d9ccd5e2da8d18fd5e4f5bd851522bf309c6e6215baeb251572c09","last_reissued_at":"2026-05-18T00:45:37.612740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:37.612740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Irreducible characters of $3'$-degree of finite symmetric, general linear and unitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eugenio Giannelli, Joan Tent, Pham Tiep","submitted_at":"2017-04-25T08:22:37Z","abstract_excerpt":"Let $G$ be a finite symmetric, general linear, or general unitary group defined over a field of characteristic coprime to $3$. 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