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We determine the universal deformation rings $R(S_5,V)$ and $R(\\hat{S}_5,V)$ for each mod 2 representation $V$ of $S_5$ that belongs to the principal 2-modular block of $S_5$ and whose stable endomorphism ring is given by scalars when it is inflated to $\\hat{S}_5$. We show that for these $V$, a question raised by the first author and Chinburg concerning the relation of the universal deformation ring of $V$ to the Sylow 2-subgroups"},"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":"0904.0031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-03-31T23:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"2cc0920a5f324c4a6e84df84efdcfec68594d5cf48718c9aaccbd46cdd28b4c9","abstract_canon_sha256":"ce13b7586561d3e8b60157b792d0e9e960e5e987297a1a5f3fe286bc0e83d2da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:49.969245Z","signature_b64":"EMtFPwFqPYY/7hn5eYBQ5UOxHHMpqhKOOM1EBZuiSSxBLJhADy/1esaOK/7Y1FjQJBQvsb9CALAOa/YZAcpoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c274c04b9b0c3b74be59394a5ad2475dda0f7a09cf8b55d754723c64f6311dd","last_reissued_at":"2026-05-18T04:33:49.968608Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:49.968608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal deformation rings for the symmetric group S_5 and one of its double covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Frauke M. 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