{"paper":{"title":"On Integral Forms of Specht Modules Labelled by Hook Partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Susanne Danz, Tommy Hofmann","submitted_at":"2017-06-09T08:03:37Z","abstract_excerpt":"We investigate integral forms of simple modules of symmetric groups over fields of characteristic $0$ labelled by hook partitions. Building on work of Plesken and Craig, for every odd prime $p$, we give a set of representatives of the isomorphism classes of $\\mathbb{Z}_p$-forms of the simple $\\mathbb{Q}_p \\mathfrak{S}_n$-module labelled by the partition $(n-k,1^k)$, where $n\\in\\mathbb{N}$ and $0\\leq k\\leq n-1$. We also settle the analogous question for $p=2$, assuming that $n\\not\\equiv 0\\pmod{4}$ and $k\\in\\{2,n-3\\}$. As a consequence this leads to a set of representatives of the isomorphism cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02860","kind":"arxiv","version":2},"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"}