{"paper":{"title":"On permutation modules and decomposition numbers for symmetric groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eugenio Giannelli","submitted_at":"2014-04-17T16:38:16Z","abstract_excerpt":"We study the indecomposable summands of the permutation module obtained by inducing the trivial $\\mathbb{F}(S_a\\wr S_n)$-module to the full symmetric group $S_{an}$ for any field $\\mathbb{F}$ of odd prime characteristic $p$ such that $a<p\\leq n$. In particular we characterize the vertices of such indecomposable summands. As a corollary we will disprove a modular version of Foulkes' Conjecture.\n  In the second part of the article we will use this information to give a new description of some columns of the decomposition matrices of symmetric groups in terms of the ordinary character of the Foul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4578","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"}